Category: Class 6

Students can download 6th Science Term 2 Chapter 1 Heat Questions and Answers, Notes, Samacheer Kalvi 6th Science Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Science Solutions Term 2 Chapter 1 Heat

Samacheer Kalvi 6th Science Heat Text Book Back Questions and Answers

I. Choose the correct answer:

Question 1.
When an object is heated, the molecules that make up the object
(a) begin to move faster
(b) lose energy
(c) become heavier
(d) become lighter
Answer:
(a) begin to move faster

Question 2.
The unit of heat is
(a) newton
(b) joule
(c) volt
(d) Celsius
Answer:
(b) joule

Question 3.
One litre of water at 30°C is mixed with one litre of water at 50°C. The temperature of the mixture will be
(a) 80°C
(b) More than 50°C but less than 80°C
(c) 20°C
(d) around 40°C
Answer:
(d) around 40° C

Question 4.
An iron ball at 50°C is dropped in a mug containing water at 50°C. The heat will
(a) flow from iron ball to water.
(b) not flow from iron ball to water or from water to iron ball.
(c) flow from water to iron ball.
(d) increase the temperature of both.
Answer:
(b) not flow from iron ball to water or from water to iron ball.

II. Fill in the Blanks

1. Heat flows from a ……….. body to a ………… body.
2. The hotness of the object is determined by its ………..
3. The SI unit of temperature is …………
4. Solids ……….. on heating and ………… on cooling.
5. Two bodies are said to be in the state of thermal ………… if there is no transfer of heat taking place.

Answer:

1. hot, cold
2. temperature
3. Kelvin
4. expand, contract
5. equilibrium

III. True or False. If False, give the correct answer.

1. Heat is a kind of energy that flows from a hot body to a cold body.
2. Steam is formed when heat is released from water.
3. Thermal expansion is always a nuisance.
4. Borosilicate glass do not expand much on being heated.
5. The unit of heat and temperature are the same.

Answer:

1. True
2. False – Steam is formed when the heat is absorbed from the water.
3. False – Thermal expansion is always not a nuisance.
4. True
5. False – Unit of heat and temperature are different.

IV. Give reasons for the following

Question 1.
An ordinary glass bottle cracks when boiling water is poured into it, but a borosilicate glass bottle does not.
Answer:
The reason is that the borosilicate glass does not expand much on being heated and therefore they do not crack.

Question 2.
The electric wire which sag in summer become straight in winter.
Answer:

1. During summer thermal expansion takes place in electric wire.
2. In winter it contracts so it becomes straight.

Question 3.
Rivet is heated before fixing in the hole to join two metal plates.
Answer:

1. When we heat rivet expansion takes place and becomes soft.
2. One end of the rivet is hammered to form a new head.
3. When cooled, the rivet will contract and hold tightly.

V. Match the following

Answer:
1. – e
2. – c
3. – d
4. – a
5. – b

VI. Analogy

1. Heat: Joule :: Temperature : ………
2. Ice cube : 0°C :: Boiling water : ………..
3. Total Kinetic Energy of molecules: Heat:: Average Kinetic Energy : …………….

Answer:

1. Kelvin
2. 100° C
3. Temperature

VII. Give Very Short Answer:

Question 1.
Make a list of electrical types of equipment at home from which we get heat.
Answer:
Water heater, Iron box, Electric kettle, Micro oven.

Question 2.
What is the temperature?
Answer:
The measurement of the warmness or coldness of a substance is known as its temperature.

Question 3.
What is thermal expansion?
Answer:
The expansion of a substance on heating is called thermal expansion.

Question 4.
What do you understand by thermal equilibrium?
Answer:
When two objects in thermal contact, no longer affect each other’s temperature, there exists Thermal equilibrium.

VIII. Give Short Answer:

Question 1.
What difference do you think heating the solid will make in their molecules?
Answer:

1. When we heat solids the vibrations and movement of molecules will increase.
2. The temperature of the object increases.
3. The distance between molecules will increase.

Question 2.
Distinguish between heat and temperature.
Answer:

IX. Answer in detail:

Question 1.
Explain thermal expansion with suitable examples.
Answer:
Thermal expansion: The expansion of a substance on heating is called, the thermal expansion of that substance.

Fitting the iron rim on the wooden wheel:

1. The diameter of the iron ring is slightly less than that of the wooden wheel.
2. So, it cannot be easily slipped on from the rim of a wooden wheel.
3. The iron ring is, therefore, first heated to a higher temperature so that it expands in size and the hot ring is then easily slipped over to the rim of the wooden wheel.
4. Coldwater is now poured on the iron ring so that it contracts in size and holds the wooden wheel tightly.

Rivetting:

1. Rivets are used to join two steel plates together.
2. Hot rivet is driven through the hole in the plates.
3. One end of the rivet is hammered to form a new rivet head.
4. When cooled, the rivet will contract and hold the two plates tightly together.

Cracking of a thick glass tumbler:

1. Glass is a poor conductor of heat.
2. When hot liquid is poured into the tumbler, the inner surface of the tumbler becomes hot and expands while the outer surface remains at room temperature and does not expand.
3. Due to this unequal expansion, the tumbler cracks.

X. Questions based on Higher Order Thinking Skills

Question 1.
When a window is accidentally left open on a winter night, will you feel uncomfortable because the cold is getting in, or because the heat is escaping from the room?
Answer:

1. When a window is left open on a winter night I will feel uncomfortable because the heat is escaping from the room.
2. The heat will transfer from high temperature to low temperature.
3. During winter cold air enters the room, so room temperature will decrease.

Question 2.
Suppose your normal body temperature was lower than what it is. How would the sensation of hot and cold change?
Answer:

1. When our body temperature is lower than normal temperature, We feel hot from the surrounding.
2. Because the surrounding temperature will be high compare to our body.

Question 3.
If you heat a circular disk with a hole, what change do you expect in the diameter of the hole? Remember that the effect of heating increases the separation between any pair of particles.
Answer:
Many of us “expect” that the diameter of the hole will decrease because the circular disk is free to expand in all directions as well. Note that expansion of metal due to heating is not like gas spreading out wherever space is available. The correct way to think about it is as follows: Hole size is irrelevant in this case. So we can think that hole is very large.

If we carve a hole so large that its radius is slightly less than that of the circular disk itself, then we will have a ring. It is obvious that the radius of the ring will increase, as atoms have more energy so their oscillation amplitude will increase. As the diameter of the ring increases, the diameter of the hole will also increase.

For example, if you want to insert one hallow pipe inside another hollow pipe of the same diameter, just heat anyone and insert the second one into the heated pipe. This explains the answer in an easy way. So it says that diameter will increase with increasing temperature.

Samacheer Kalvi 6th Science Heat Additional Important Questions and Answers

I. Choose the right answer:

Question 1.
When an electric current is passing through the conductor …………… energy is produced.
(a) Electric
(b) Heat
(c) Chemical
(d) Kinetic energy
Answer:
(b) Heat

Question 2.
One day in 1922, the air temperature was measured at 59°C in the shade in Libya ________
(a) America
(b) Africa
(c) Antarctica
(d) Europe
Answer:
(b) Africa

Question 3.
The temperature of boiling water is …………..
(a) 0° C
(b) 32° C
(c) 100° C
(d) 110° C
Answer:
(c) 100°C

Question 4.
The temperature determines the direction flow of _______
(a) heat energy
(b) kinetic energy
(c) potential energy
(d) light energy
Answer:
(a) heat energy

Question 5.
When we cool the liquid it will become …………..
(a) Gas
(b) Solid
(c) Vapour
(d) None
Answer:
(b) Solid

II. Say True or False.

1. Heat is measured in Celsius or centigrade.
2. Temperature in the form of energy.
3. The normal temperature of our body is 37°C.
4. Two objects are said to be in thermal contact if they can exchange heat energy.
5. When the vibrations move from one molecule to another molecule heat will flow.

Answer:

1. False
2. False
3. True
4. True
5. True

III. Match the Following:

Answer
1. – iv
2. – i
3. – ii
4. – v
5. – iii

IV. Analogy

1. Summer : Sag :: Winter : …………
2. Evaporation : 100°C :: Freezing : …………

Answer:

1. contract
2. 0°C

V. Give reasons for the following:

Question 1.
Gaps are left in between rails while laying a railway track.
Answer:
Reason: During summer thermal expansion takes place.

Question 2.
Hot metal ball of 80° C is dipped into water of 80°C. The ball will not contract.
Answer:
Reason: Both are in same temperature.

VI. Very Short Answer:

Question 1.
What are the sources of heat?
Answer:

1. The main source of heat is Sun.
2. Other sources are combustion, friction and electricity.

Question 2.
Define – heat.
Answer:
Heat is an energy that raises the temperature of a thing by causing the molecules in that thing to move faster.

Question 3.
How will you identify two objects are said to be in thermal equilibrium?
Answer:
Two objects in thermal contact have same temperature they are said to be in thermal equilibrium.

Question 4.
What are the measuring unit of temperature?
Answer:
SI unit of temperature is kelvin. Celsius and Fahrenheit are the other units used.

Question 5.
What will determine the direction of flow of heat from one object to another?
Answer:
Temperature will determine the direction of the flow of heat.

VII. Long Answer Questions:

Question 1.
Explain linear expansion with an experiment.
Answer:

1. The expansion in length is called linear expansion.
2. Take a bulb, dry cell, candle, cycle spoke, coin, and two wooden boxes.
3. Place one end of the cycle spoke on a wooden block and connect an electric wire to it. Put a stone over the spoke to hold it.
4. The other one of the cycle spoke is placed on another wooden block.
5. Wrap some electric wire around the coin and place it on the block. Put a stone over the coin to hold it in place.
6. Connect bulb and dry cell to the free ends of wires connected to the coin and the spoke and make the circuit.
7. When we heat the cycle spoke with a candle the length will expand and touches the coin.
8. So the circuit completes, the bulb will glow.
9. When we cool the spoke it contracts and does not touch the coin. So the circuit will disconnect, the bulb will not glow.

Students can download 6th Science Term 1 Chapter 7 Computer – An Introduction Questions and Answers, Notes, Samacheer Kalvi 6th Science Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Science Solutions Term 1 Chapter 7 Computer – An Introduction

Samacheer Kalvi 6th Science Computer – An Introduction Text Book Back Questions and Answers

I. Choose the correct answer:

Question 1.
Who is the father of computer?
a. Martin Luther King
b. Graham Bell
c. Charlie Chaplin
d. Charles Babbage
Answer:
d. Charles Babbage

Question 2.
Which of the following is another form of computer?
(a) Blackboard
(b) Mobile
(c) Radio
(d) Book
Answer:
(b) Mobile

Question 3.
When was the first computer introduced?
a. 1980
b. 1947
c. 1946
d. 1985
Answer:
c. 1946

Question 4.
Who is the computer’s first programmer?
(a) Lady Wellington
(b) Augusta ado Lovelace
(c) Mary Curie
(d) Mary Comb
Answer:
(b) Augusta ado Lovelace

Question 5.
Pick out the odd one?
a. Calculator
b. Abacus
c. Flash Card
d. Laptop
Answer:
c. Flash Card

II. Fill in the blanks:

1. Data is ………… Information.
2. World’s first general purpose computer is ……….
3. Information is ……… data
4. Fifth generation computer has ………. Intelligence.
5. ………… is the device that uses Index number.

Answer:

1. Processed
2. Electronic Numerical Integrator and computer
3. a form of processed
4. Artificial
5. Analog Computer

III. State True or false.

1. The computer is an Electronic device.
2. Sir Isaac Newton invented the Computer.
3. The computer can do calculations fast.

Answer:

1. True
2. False
3. True

IV. Match the following:

Answer:
1. – c
2. – d
3. – b
4. – e
5. – a

V. Answer the following

Question 1.
What is a Computer?
Answer:
Computer is an electronic device that processes data and information according to our needs.

Question 2.
Who are the pioneers/forerunners of computers?
Answer:
1. Charles Babbage: a professor in mathematics has designed an analog computer. He is known as the father of computers.
2. Augusta Ada Lovelace: the first programmer as she developed essential commands for mathematical operations.

Question 3.
Write a short note on Data.
Answer:

1. Data is the information that has to be processed.
2. They are in the form of numbers, alphabets, and images.

Question 4.
Name any four input devices.
Answer:
Keyboard, Mouse, Bar code reader, Digital camera, etc.

Question 5.
Differentiate Hardware and Software.
Answer:
Hardware: The parts that are available on the computer that helps the software to work.
Software: The commands or programs that are used on a computer.

VI. Answer in Details.

Question 1.
Explain in detail the Applications of the computer.
Answer:

1. The computer is used in textile shops for billing purposes.
2. It is used in the railway station for issuing tickets.
3. It is used in the banks for multi-purpose.
4. It is used in ATMs.
5. It is used in the Post office.

Students can download 6th Science Term 1 Chapter 6 Health and Hygiene Questions and Answers, Notes, Samacheer Kalvi 6th Science Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Science Solutions Term 1 Chapter 6 Health and Hygiene

Samacheer Kalvi 6th Science Health and Hygiene Text Book Back Questions and Answers

I. Choose the correct answer:

Question 1.
Our body needs for muscle-building
(a) Carbohydrate
(b) fat
(c) Protein
(d) Water
Answer:
(c) Protein

Question 2.
Scurvy is caused due to the deficiency of _______
(a) Vitamin A
(b) Vitamin B
(c) Vitamin C
(d) Vitamin D
Answer:
(c) Vitamin C

Question 3.
Calcium is an example of a
(a) Carbohydrate
(b) fat
(c) Protein
(d) minerals
Answer:
(d) minerals

Question 4.
We should include fruits and vegetables in our diet, because _______
(a) They are the best source of Carbohydrates
(b) They are the best source of Proteins
(c) They are rich in minerals and Vitamins
(d) They have high water content
Ans:
(c) They are rich in minerals and Vitamins

Question 5.
Bacteria are very small microorganism.
(a) Prokaryotic
(b) Eukaryotic
(c) Protozoa Acellular
(d) Acellular
Answer:
(a) prokaryotic

II. True or False

1. There are three main nutrients present in food.
2. Fats are used as an energy store by our body.
3. All bacteria have flagella.
4. Iron helps in the formation of haemoglobin.
5. Virus can grow and multiply outside host.

Answer:

1. False
2. True
3. False
4. True
5. False

III. Fill in the blanks

1. Malnutrition leads to …………
2. Iodine deficiency leads to ……… in adults.
3. Vitamin D deficiency causes ………..
4. Typhoid is transmitted due to contamination of ……….. and water.
5. Influenza is a ………. disease.

Answer:

1. Deficiency diseases
2. Goitre
3. Rickets and water.
4. Food
5. Viral

IV. Complete the Analogy

1. Rice: Carbohydrate : : Pulses: …………
2. Vitamin D: Rickets : : Vitamin C: …………..
3. Iodine: Goitre : : Iron: ……………
4. Cholera: Bacteria : : Smallpox: ………….

Answer:

1. Protein
2. Scurvy
3. Anemia
4. Virus

V. Match the Following

Answer:
1. – b
2. – d
3. – e
4. – a
5. – c

VI. Complete the Diagram

Answer:

VII. Write a Short Answer.

Question 1.
Write two examples for each of the following.
(a) Food items rich in fat.
(b) Vitamin deficiency diseases.
Answer:
(a) Food items rich in fat: Meat, fish, egg yolk, milk.
(b) Vitamin deficiency diseases: Night blindness, Beriberi, Scurvy, Rickets.

Question 2.
Differentiate between Carbohydrate and Protein.
Answer:
Carbohydrate:

1. Energy giving component of the food.
2. The sources of carbohydrates are nuts, fruits, rice, and maize.

Protein:

1. It is body building foods.
2. The sources of proteins are pulses, soybean, nuts, egg, and fish.

Question 3.
Define the term “Balanced diet”.
Answer:
A diet which contains a sufficient amount of various nutrients to ensure good health is called a Balanced diet.

Question 4.
Why should the fruits and vegetables not to be washed after cutting? Vitamins are of two types.
Answer:
We should not wash the fruits and vegetables after cutting, because the minerals and protein in the fruits and vegetables will also be washed away.

Question 5.
Write any two viral diseases.
Answer:
Common cold, smallpox, polio are viral diseases.

Question 6.
What are the main features of a microorganism?
Answer:
Microorganism will be seen with the help of a microscope. They are very small in size.

VIII. Long Answers.

Question 1.
Tabulate the vitamins and their corresponding deficiency diseases.
Answer:

Samacheer Kalvi 6th Science Health and Hygiene Additional Important Questions and Answers

I. Choose the best options

Question 1.
Name the sunshine Vitamin
(a) A
(b) D
(c) C
(d) K
Answer:
(b) D

Question 2.
_______ is a highly rich source of protein.
(a) Nut
(b) Gram
(c) Chicken
(d) Soya bean
Answer:
(d) Soya bean

Question 3.
The minerals are called by this name:
(a) Energy Food
(b) Balance diet
(c) Food for growth
(d) protective food
Answer:
(d) protective food

Question 4.
Ben Ben is caused due to the deficiency of _______
(a) Vitamin C
(b) Vitamin D
(c) Vitamin K
(d) Vitamin B
Ans:
(d) Vitamin B

Question 5.
How much water is needed for a man in a day?
(a) 2L
(b) 3L
(c) 1.5L
(d) 1L
Answer:
(a) 2 lr

II. Matching

Answer:
1. – d
2. – c
3. – b
4. – a

III. Give Short Answers.

Question 1.
Define Nutrients.
Answers:
Chemical constituents of food which give us energy, help to build our body, and protect us from diseases are called Nutrients.

Question 2.
List the six important nutrition.
Answer:

1. Carbohydrate
2. Vitamins
3. Protein
4. Minerals
5. Fat
6. Water.

Question 3.
List out the types of vitamins.
Solution:
Vitamins are classified into six major types. They are Vitamin A, B, C, D, E, and K. In the type,
Vitamin B and C are water-soluble Vitamins
Vitamin A, D, E, K are Fat-soluble vitamins.

Question 4.
Differentiate between Kwashiorkor and Marasmus.
Answer:
Kwashiorkor:
Stunted growth.
Swelling of face and limbs diarrhea.

Marasmus:
Skinny appearance.
slow body growth.

Question 5.
What are food items contain minerals?
Answer:
Green leafy vegetables like spinach, pulses, eggs, milk, fish, and fruits are food items that contain minerals.

IV. Give detailed Answers

Question 1.
Fill ABCDE in this tabular column.
Answer:

Question 2.
What are the uses of exercise?
Answer:

1. It improves growth and development.
2. It delays aging.
3. It strengthens muscles and blood circulation.
4. It develops athletic skills and reduces weight.

Students can download Maths Chapter 2 Integers Ex 2.2 Questions and Answers, Notes, Samacheer Kalvi 6th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 2 Integers Ex 2.2

Miscellaneous Practice Problems

Question 1.
Write two different real-life situations that represent the integer -3.
Solution:
(i) A sapling planted at a depth of 3m
(ii) Sheela lost ₹ 3 on selling an apple.

Question 2.
Mark the following numbers on a number line.
(i) All integers which are greater than -7 but less than 7.
(ii) The opposite of 3.
(iii) 5 units to the left of -1.
Solution:

Question 3.
Construct a number line that shows the depth of 10 feet from the ground level and its opposite.
Solution:

Question 4.
identify the integers and mark on the number line that are at a distance of 8 units from – 6.
Solution:

Question 5.
Answer the following questions from the number line given below.

(i) Which integer is greater: G or K? Why?
(ii) Find the integer that represents C
(iii) How many integers are there between G and H?
(iv) Find the pairs of letters which are opposite of a number,
(v) Say True or False: 6 units to the left of D is -6.
Solution:
(i) K is greater. K represents -1 and G represents -3. Because it is to the right of G in the negative side of the number line.
(ii) C represents -4
(iii) G represents -3 and H represents 4.
∴ -2, -1, 0, 1, 2, 3 are the 6 numbers between G and H.
(iv) (C, H) and (E, J) are opposite pairs.
(v) False. 6 units to the left of D is 0. Because D represents +6 on the number line

Question 6.
If G is 3 and C is -1, what numbers are A and K on the number line?

Solution:
A (-3), K (7)

Question 7.
Find the integers that are 4 units to the left of 0 and 2 units to the right of -3?
Solution:
-4, -1

Challenge Problems

Question 8.
Is there the smallest and the largest number in the set of integers? Give reason.
Solution:
No, we cannot find the smallest (-) and largest (+) number in the set of integers, as the numbers on the number line extend on both sides without an end.

Question 9.
Look at the Celsius Thermometer and answer the following questions.

(i) What is the temperature that is shown in the Thermometer?
(ii) Where will you mark the temperature 5°C below 0° C in the Thermometer?
(iii) What will be the temperature, if 10° C is reduced from the temperature shown in the Thermometer?
(iv) Mark the opposite of 15° C in the Thermometer.
Solution:
(i) – 10°C
(ii) – 5°C
(iii) -20°C
(iv) -15°C

Question 10.
P, Q, R, and S are four different integers on a number line. From the following clues, find these integers and write them in ascending order.
(i) S is the least of the given integers.
(ii) R is the smallest positive integer.
(iii) The integers P and S are at the same distance from 0.
(iv) Q is 2 units to the left of integer R.
Solution:
S < Q < 0 < R < P

Question 11.
Assuming that the home to be the starting point, mark the following places in order on the number line as per instruction given below and write their corresponding integers.

Places: Home, School, library, Playground, Park, Departmental Store, Bus stand, Railway Station, Post Office, Electricity Board.
Instructions:

1. The bus stand is 3 units to the right of the Home.
2. The library is 2 units to the left of Home.
3. Departmental Store is 6 units to the left of Home.
4. The post office is 1 unit to the right of the Library.
5. Park is 1 unit right of Departmental Store.
6. Railway Station is 3 units left of Post Office.
7. Bus Stand is 8 units to the right of Railway Station.
8. School is next to the right of the Bus Stand.
9. Playground and Library are opposite to each other.
10. Electricity Board and Departmental Store are at equal distance from Home.

Solution:

1. 3
2. -2
3. -6
4. -1
5. -5
6. -4
7. 4
8. 4
9. 5
10. 2

Question 12.
Complete the table using the following hints.

(i) C1 : the first non-negative integer.
(ii) C3 : the opposite to the second negative integer.
(iii) C5 : the additive identity in whole numbers.
(iv) C6 : the successor of the integer in C2.
(v) C8 : the predecessor of the integer in C7.
(vi) C9 : the opposite to the integer in C5.
Solution:
(i) C1 : (0)
(ii) C3 : (2)
(iii) C5 : (0)
(iv) C6 : (-4)
(v) C8 : (-8)
(vi) C9 : (0)

Question 13.
The following bar graph shows the profit (+) and loss (-) of a small scale company (in crores) between the year 2011 to 2017.

(i) Write the integer that represents a profit or a loss for the company in 2014?
(ii) Denote by an integer on the profit or loss in 2016.
(iii) Denote by integers on the loss for the company in 2011 and 2012.
(iv) Say True or False: The loss is minimum in 2012.
(v) Fill in: The amount of loss in 2011 is _____ as profit in 2013.
Solution:
(i) Profit ₹ 45 crores. ∴ Ans : + 45
(ii) In 2016 neither profit nor loss happened. ∴ Ans : 0
(iii) In 2011 loss is 10 crores and in 2012 loss is 20 crores.
∴ -10 and-20.
(iv) False. In 2011 the company’s loss is minimum.
(v) The same. Because in 2013 the profit is 10 crores and in 2011 the loss is 10 crores.

Students can download Maths Chapter 5 Information Processing Ex 5.2 Questions and Answers, Notes, Samacheer Kalvi 6th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.2

Miscellaneous Practice Questions 

Question 1.
Find HCF of 188 and 230 by Euclid’s game.
Solution:
By Euclid’s game HCF (a, b) = HCF (a, a – b) if a > b.
Here HCF (188, 230) = HCF (230, – 188) because 230 > 188
= HCF (188, 42) = HCF (146, 42)
= HCF (104, 42) = HCF (62, 42)
= HCF (42, 20) = HCF (22, 20)
= HCF (20,2) = HCF (18, 2) = 2
∴ HCF (230, 188) = 2

Question 2.
Write the numbers from 1 to 50. From that find the following.
i) The numbers which are neither divisible by 2 nor 7.
ii) The prime numbers between 25 and 40
iii) All square numbers upto 50.
Solution:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50.
i) The numbers neither divisible by 2 nor 7 are 9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 31, 33, 37, 39, 41, 43, 45, 47.
ii) The prime numbers between 25 and 40 are 29, 31, 37.
iii) Square numbers upto 50 are 1, 4, 9, 16, 25, 36, 49

Question 3.
Complete the following pattern.
(i) 1 + 2 + 3 + 4 = 10
2 + 3 + 4 + 5 = 14
___ + 4 + 5 + 6 = ___
4 + 5 + 6 + ___ = ___

(ii) 1 + 3 + 5 + 7 = 16
___ + 5 + 7 + 9 = 24
5 + 7 + 9 + ___ = ___
7 + 9 + ___ + 13 = ___

(iii) AB, DEF, HIJK, ___ , STUVWX
(vi) 20, 19, 17, ___ , 10, 5
Solution:
(i) 3, 18; 7, 22
(ii) 3; 11, 32; 11, 40
(iii) MNOPQ
(iv) 14

Question 4.
Complete the table by using the following instructions.

A : It is the 6th term in the Fibonacci sequence.
B : The predecessor of 2.
C : LCM of 2 and 3.
D : HCF of 6 and 20.
E : The reciprocal of 1/5.
F : The opposite number of -7.
G : The first composite number.
H : Area of a square of side 3 cm.
I : The number of lines of symmetry of an equilateral triangle.
After completing the table, what do you observe? Discuss.
Solution:
A – 8, B – 1, C – 6, D – 2, E – 5, F – 7, G – 4, H – 9, I – 3

Question 5.
Assign the number for English alphabets as 1 for A, 2 for B upto 26 for Z. Find the meaning of

Solution:
GOOD MORNING

Question 6.
Replace the letter with symbols as + for A, – for B, × for C, and ÷ for D. Find the answer for the pattern 4B3C5A30D2 by doing the given operations.
Solution:
Given the symbols + for A; – for B; × for C; + for D .
∴ 4B3C5A30D2 becomes
4 – 3 × 5 + 30 ÷ 2 Using BIDMAS rule
4 – 3 × 5 + 30 ÷ 2 = 4 – 3 × 5 + 15[× done first]
= 4 – 15 + 15 [+ done second]
= 4 – 0 [+ done third]
= 4 [- done last]

Question 7.
Observe the pattern and find the word by hiding the Numbers 1 H 2 0 3 W, 4 A 5 R 6 E, 7 Y 8 0 9 U.
Solution:
HOW ARE YOU

Question 8.
Arrange the following from the eldest to the youngest. What do you get?

Solution:
Arranging from eldest to the youngest we get
F – refers to grandparents
A – refers to parents
M – refers to an uncle
I – refers to elder sister
L – refers to me
Y – refers to the younger brother
So we get FAMILY

Challenge Problems

Question 9.
Prepare a daily time schedule for evening study at home.
Solution:
5.00 pm to 6.00 pm – Mathematics
6.0 pm to 7.00 pm – Science
7.0 pm to 8.00 pm – Social Science
8. pm to 9.00 pm – Dinner & Recreation
9. pm to 10.00 pm – Tamil and English

Question 10.
Observe the geometrical pattern and answer the following questions.

(i) Write down the number of sticks used in each iterative pattern,
(ii) Draw the next figure in the pattern also find the total number of sticks used in it.
Solution:
(i) 3, 9, 18

Question 11.
Find the HCF of 28, 35, 42 by Euclid’s game.
Solution:
HCF of 28, 35, 42
HCF of (28, 35 – 28, 42 – 28)
28 = 2 × 2 × 7
7 = 1 × 7
14 = 2 × 7
HCF of (28, 7, 14) = 7

Question 12.
Follow the given instructions to fill your name in the OMR sheet.
1. The name should be written in capital letters from left to right.
2. One alphabet is to be entered in each box.
3. If any empty boxes are there at the end they should be left blank.
4. Ballpoint pen is to be used for shading the bubbles for the corresponding alphabets.

Solution:
Do your self.

Question 13.
Consider the Postal index number (PIN) written on the letters as follows: 604506; 604516; 604560; 604506; 604516; 604516; 604560; 604516; 604505; 604470; 604515; 604520; 604303; 604509; 604470. How the letters can be sorted as per Postal Index Numbers?
Solution:
604 is common for all postal index numbers. Compare the remaining 3 digits, 303, 470, 505, 506 (two) 509, 510. 515, 516 (Four), 520, 560 (two).

Students can download Maths Chapter 5 Information Processing Ex 5.1 Questions and Answers, Notes, Samacheer Kalvi 6th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1

Question 1.
Study and complete the following pattern.
(i) 1 × 1 = 1
11 × 11 = 121
111 × 111 = 12321
1111 × 1111 = ?
11111 × 11111 = ?

Solution:
(i) 1234321, 123454321
(ii) 144, 60, 84, 36, 48, 15, 27

Question 2.
Find next three numbers in the following number patterns.
(i) 50, 51, 53, 56, 60……
(ii) 77, 69, 61, 53, ……
(iii) 10, 20, 40, 80,…
(iv) \(\frac{21}{33}\), \(\frac{321}{444}\), \(\frac{4321}{555}\)
Solution:

i) The pattern generating these numbers is
50, 50 + 1, 51 + 2, 53 + 3, 56 + 4, 60 + 5, 65 + 6, 71 + 7,
∴ 50, 51, 53, 56, 60, 65, 71, 78, ……
∴ The next three numbers will be 65, 71, 78

ii) The pattern generating these numbers is
77, 77 – 8, 69 – 8, 61 – 8, 53 – 8, 45 – 8, 37 – 8, 29
77, 69, 61, 53, 45, 37, 29, 21,
∴ The next three numbers will be 45, 37, 29.

iii) The pattern generating these numbers is
10, 10 + 10, 20 + 20, 40 + 40, 80 + 80, 160 + 160, 320 + 320,….
10, 20, 40, 80, 160, 320, 640,….
∴ The next three numbers will be 160, 320, 640.

(iv) \(\frac{54321}{66666}\), \(\frac{654321}{777777}\), \(\frac{7654321}{8888888}\)

Question 3.
Consider the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,…. Observe and complete the following table by understanding the number patterns? followed. After filling the table discuss the pattern followed in addition and subtraction, of the numbers of the sequence?

Solution:
(i) 12, 13 – 1 = 12
(ii) 33, 34 – 1 = 33
(iii) 1 + 3 + 8 + 21 + 55 = 88, 89 – 1 = 88

Question 4.
Complete the following patterns.

Solution:

Question 5.
Find the HCF of the following pair of numbers by Euclid’s game
(i) 25 and 35
(ii) 36 and 12
(iii) 15 and 29
Solution:
(i) HCF of (25, 35 – 25)
25 = 5 × 5
10 = 2 × 5
HCF of (25, 10) = 5

(ii) HCF of (36, 36 – 12)
36 = 2 × 2 × 3 × 3
24 = 2 × 2 × 2 × 3
HCF of (36, 24) = 2 × 2 × 3 = 12

(iii) HCF of (15, 29 -15)
15 = 3 × 5 × 1
14 = 2 × 7 × 1
HCF of (15, 14) = 1

Question 6.
Find HCF of 48 and 28. Also find the HCF of 48 and the number obtained by finding their difference.
Solution:
HCF of 48 and 28
48 = 2 × 2 × 2 × 2 × 3
28 = 2 × 2 × 7
HCF of (48, 28) = 2 × 2 = 4
HCF of (48, 48 – 28)
48 = 2 × 2 × 2 × 2 × 3
20 = 2 × 2 × 5
HCF of (48, 20) = 4

Question 7.
Give instructions to fill in a bank withdrawal form issued in a bank.
Solution:

• The name should be written in capital letters from left to right.
• Write the date of withdrawal on the right top comer of the form.
• Write the amount (in words) to be withdrawn in the space provided.
• Write the amount (in figures) to be withdrawn in the box provided.
• Put your signature at the right bottom above the ‘signature of the depositor’.

Question 8.
Arrange the name of your classmates alphabetically.
Solution:

Question 9.
Follow and execute the instructions given below.

(i) Write the number 10 in the place common to the three figures
(ii) Write the number 5 in the place common for square and circle only.
(iii) Write the number 7 in the place common for triangle and circle only.
(iv) Write the number 2 in the place common for triangle and square only.
(v) Write the numbers 12, 14, and 8 only in square, circle, and triangle respectively.
Solution:

Question 10.
Fill in the following information

Solution:

Objective Type Questions

Question 11.
The next term in the sequence 15, 17, 20, 22, 25, … is
(a) 28
(b) 29
(c) 27
Hint:
Add 2 and 3 alternatively
Solution:
(c) 27

Question 12.
What will be the 25th letter in the pattern? ABCAABBCCAAABBBCCC,…
(a) B
(b) C
(c) D
(d) A
Solution:
(a) B

Question 13.
The difference between 6th term add 5th term in the Fibonacci sequence is ___.
(a) 6
(b) 8
(c) 5
(d) 3
Solution:
(d) 3

Question 14.
The 11th term in the Lucas sequence 1, 3, 4, 7, is
(a) 199
(b) 76
(c) 123
(d) 47
Solution:
(a) 199

Question 15.
If the Highest Common Factor of 26 and 54 is 2, then HCF of 54 and 28 is .
(a) 26
(b) 2
(c) 54
(d) 1
Hint: HCF (54, 28) = HCF (28, 26) = 2
Solution:
(b) 2

Students can download Maths Chapter 4 Symmetry Ex 4.2 Questions and Answers, Notes, Samacheer Kalvi 6th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 4 Symmetry Ex 4.2

Miscellaneous Practice Problems

Question 1.
Draw and answer the following.
(i) A triangle which has no line of symmetry.
(ii) A triangle which has only one line of symmetry
(iii) A triangle which has three lines of symmetry.
Solution:
(i) Scalene triangle
(ii) Isosceles triangle
(iii) Equilateral triangle

Question 2.
Find the alphabets in the box which have

(i) No line of symmetry
(ii) Rotational symmetry
(iii) Reflection symmetry
(iv) Reflection and rotational symmetry.
Solution:
i) The alphabets which have no line of symmetry are P, N, S, Z
ii) The alphabets which have Rotational symmetry are I, O, N, X, S, H, Z
iii) The alphabets which have reflection symmetry are A, M, E, D, I, K, O, X, H, U, V, W.
iv) The alphabets which has reflection and rotational symmetry are I, O, X, H.

Question 3.
For the following pictures, find the number of lines of symmetry and also find the order of rotation.

Solution:
(i) 0, 2
(ii) 1, 0
(iii) 2, 2
(iv) 8, 8
(v) 1, 0

Question 4.
The three-digit number 101 has rotational and reflection symmetry. Give five more examples of three-digit numbers that have both rotational and reflection symmetry
Solution:
The digits 0, 1, 8 have rotational and reflection symmetry.
∴ The three digits numbers 181, 111, 808, 818, 888 have both rotational and reflection symmetry.

Question 5.
Translate the given pattern and complete the design in a rectangular strips?

Solution:

Challenge Problems

Question 6.
Shade one square so that it possesses

(i) One line of symmetry
(ii) Rotational symmetry of order 2
Solution:

Question 7.
Join six identical squares so that atleast one side of a square fits exactly with any other side of the square and has reflection symmetry (any three ways).
Solution:

Question 8.
Draw the following
(i) A figure which has reflection symmetry but no rotational symmetry.
(ii) A figure which has rotational symmetry but no reflection symmetry.
(iii) A figure which has both reflection and rotational symmetry.
Solution:

Question 9.
Find the line of symmetry and the order of rotational symmetry’ of the given regular polygons and complete the following table and answer the questions given below.

i) A regular polygon of 10 sides will have ______ lines of symmetry.
ii) If a regular polygon has 10 lines of symmetry then its order of rotational symmetry is ______
iii) A regular polygon of ‘n’ sides has lines of symmetry and the order of rotational symmetry is ______
Solution:
(i) 10
(ii) 10
(iii) n, n

Question 10.
Colour the boxes in such a way that it possesses translation symmetry.

Solution:

Students can download Maths Chapter 4 Symmetry Ex 4.1 Questions and Answers, Notes, Samacheer Kalvi 6th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 4 Symmetry Ex 4.1

Question 1.
Fill in the blanks
(i) The reflected image of the letter ‘q’ is …….
(ii) A rhombus has ………… lines of symmetry.
(iii) The order of rotational symmetry of the letter ‘Z’ is ……….
(iv) A figure is said to have rotational symmetry, if the order of rotation is atleast ……….
(v) ……… symmetry occurs when an object slides to new position.
Solution:
(i) P
(ii) two
(iii) 2
(iv) two
(v) Translation

Question 2.
Say True or False
(i) A rectangle has four lines of symmetry.
(ii) A shape has reflection symmetry if it has a line of symmetry.
(iii) The reflection of the name RANI is INAЯ.
(iv) Order of rotation of a circle is infinite.
(v) The number 191 has rotational symmetry.
Solution:
(i) False
(ii) True
(iii) False
(iv) True
(v) False

Question 3.
Match the following shapes with their number of lines of symmetry.

Solution:
(i) d
(ii) a
(iii) b
(iv) c

Question 4.
Draw the lines of symmetry of the following.

Solution:

Question 5.
Using the given horizontal line/ vertical line as a line of symmetry, complete each alphabet to discover the hidden word.

Solution:
(i) DECODE
(ii) KICK
(iii) BED
(iv) WAY
(v) MATY
(vi) TOMATO

Question 6.
Draw a line of symmetry of the given figures such that one hole coincides with the other hole(s) to make pairs.

Solution:

Question 7.
Complete the other half of the following figures such that the dotted line is the line of symmetry.

Solution:

Question 8.
Find the order of rotation for each of the following.

Solution:
(i) 2
(ii) 2
(iii) 4
(iv) 8
(v) 2

Question 9.
A standard die has six faces which are shown below. Find the order of rotational symmetry of each face of a die?

Solution:
(i) 4
(ii) 2
(iii) 2
(iv) 4
(v) 4
(vi) 2

Question 10.
What pattern is translated in the given border kolams?

Solution:

Objective Type Questions

Question 11.
Which of the following letter does not have a line of symmetry?
(a) A
(b) P
(c) T
(d) U
Hint: A, T, U have one line of symmetry
Solution:
(b) P

Question 12.
Which of the following is a symmetrical figure?

Solution:
(c)

Question 13.
Which word has a vertical line of symmetry?
(a) DAD
(b) NUN
(c) MAM
(d) EVE
Hint: D, N, E have no vertical line of symmetry
Solution:
D, N, E have no vertical line of symmetry

Question 14.
The order of rotational symmetry of 818 is ………
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
(b) 2

Question 15.
The order of rotational symmetry ★ is ___
(a) 5
(b) 6
(c) 7
(d) 8
Solution:
(a) 5

Students can download Maths Chapter 3 Perimeter and Area Ex 3.2 Questions and Answers, Notes, Samacheer Kalvi 6th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 3 Perimeter and Area Ex 3.2

Miscellaneous Practice Problems

Question 1.
A piece of wire is 36 cm long. What will be the length of each side if we form
(i) a square
(ii) an equilateral triangle
Solution:

Given the length of the wire = 36 cm
i) When a square is formed out of it
The perimeter of the square = 36 cm
4 × side = 36
side = \(\frac{36}{4}\) = 9 cm
Side of the square

ii) When an equilateral triangle is formed out of it, its perimeter = 36 cm
i.e., side + side + side = 36 cm .
3 × side = 36 cm
side = \(\frac{36}{3}\) = 12 cm
One side of an equilateral triangle = 12 cm

Question 2.
From one vertex of an equilateral triangle with a side of 40 cm, an equilateral triangle with 6 cm side is removed. What is the perimeter of the remaining portion? The perimeter of the remaining portion
Solution:

= (40 + 34 + 6 + 34) cm
= 114 cm

Question 3.
Rahim and Peter go for a morning walk, Rahim walks around a. square path of side 50 m and Peter walks around a rectangular path with a length of 40 m and a breadth of 30 m. If both of them walk 2 rounds each, who covers more distance and by how much?
Solution:
Distance covered by Rahim
= 50 × 4 m
= 200 m
If he walks 2 rounds, distance covered = 2 × 200 m
= 400 m
Distance covered by peter
= 2 (40 + 30) m
= 2(70)m
= 140 m
If he walks 2 rounds, distance covered = 2 × 140 m
= 280 m
∴ Rahim covers more distance by (400 – 280) = 120 m

Question 4.
The length of a rectangular park is 14 m more than its breadth. If the perimeter of the park is 200 m, what is its length? Find the area of the park.
Solution:
Let the length be b + 14 m
breadth = b
perimeter = 200
2 (l + b) = 200
2 (b + 14 + b) = 200
2 (2b + 14) = 200
28 + 4b = 200
4b = 200 – 28
4b = 172 m
b = \(\frac{172}{4}\)
b = 43 m
Length = b + 14
= 43 + 14
Length l = 57 m
Area = l × b units
= 57 × 43 m²
= 2451 m²

Question 5.
Your garden is in the shape of a square of side 5 m. Each side is to be fenced with 2 rows of wire. Find how much amount is needed to fence the garden at ₹ 10 per metre.
Solution:
a = 5 m
The perimeter of the garden
= 4 a units
= 4 × 5 m
= 20 m
For 1 row
Amount needed to fence l m= Rs 10
Amount needed to fence 20 m
= Rs 10 × 20
= Rs 200
For 2 rows
Total amount needed = 2 × Rs 200 = Rs 400

Challenge Problems

Question 6.
A closed shape has 20 equal sides and one of its sides is 3 cm. Find its perimeter.
Solution:
Number of equal sides in the shape = 20
One of its side = 3 cm
Perimeter = length of one side × Number of equal sides
∴ Perimeter = (3 × 20) cm = 60 cm
∴ Perimeter = 60 cm

Question 7.
A rectangle has length 40 cm and breadth 20 cm. How many squares with side 10 cm can be formed from it.
Solution:
Area of rectangle = (length × breadth) units²
Length = 40 cm
Breadth = 20 cm
∴ Area = (40 × 20) cm² = 800 cm²
Area of rectangle = 800 cm²
Area of square = (side × side) units²
side = 10 cm
∴ Area of square = (10 × 10) cm² = 100 cm²
Required number of squares = \(\frac{\text { Area of Rectangle }}{\text { Area of } 1 \text { square }}=\frac{800 \mathrm{cm}^{2}}{100 \mathrm{cm}^{2}}\) = 8
8 squares can be formed.

Question 8.
The length of a rectangle is three times its breadth. If its perimeter is 64 cm, find the sides of the rectangle.
Solution:
Given perimeter of a rectangle = 64 cm
Also given length is three times its breadth.
Let the breadth of the rectangle = b cm
∴ Length = 3 × b cm
Perimeter = 64 m
i.e., 2 × (l + b) = 64 m
2 × (3b + b) = 64 m
2 × 4b = 64m
4b = \(\frac{64}{2}\) = 32 m
b = \(\frac{32}{4}\) = 8 m
l = 3 × b = 3 × 8 = 24 m
∴ Breadth of the rectangle = 8 m
Length of the rectangle = 24 m

Question 9.
How many different rectangles can be made with a 48 cm long string? Find the possible pairs of length and breadth of the rectangles.
Solution:
Length of the string to be made into rectangle = 48 cm
∴ Perimeter of the rectangle = 48 cm
2 × (l + b) = 48 cm
l + b = \(\frac{48}{2}\)
l + b = 24 cm
Possible pairs of length and breadth are (1, 23), (2, 22) (3, 21), (4, 20), (5, 19),
(6, 18), (7, 17), (8, 16), (9, 15), (10, 14), (11, 13), (12, 12)
Number of different rectangles = 12.

Question 10.
Draw a square B whose side is twice of the square A. Calculate the perimeters of the squares A and B.
Solution:

Perimeter of A = s + s + s + s units = 4 s units
Perimeter of B = (2s + 2s + 2s + 2s) units
= 8s units = 2 (4s) units.
∴ The perimeter of B is twice the perimeter of A

Question 11.
What will be the area of a new square formed if the side of a square is made one – fourth?
Solution:
Let the side of square is s units then area = (s × s) units²
If the side of the new square is made one fourth then side = \(\left(\frac{1 \times s}{4}\right)\) units
Then area = \(\left(\frac{1 \times s}{4} \times \frac{1 \times s}{4}\right)\) units² = \(\frac{s \times s}{16}=\frac{1}{16}\) (s × s) units²
Area of the new square is reduced to \(\frac{1}{16}\) times to that of original area.

Question 12.
Two plots have the same perimeter. One . is a square of side 10 m and another is a rectangle of breadth 8 m. Which plot has the greater area and by how much?
Solution:
a = 10 m, b = 8 m
Perimeter of the square plot
= 4 a units
= 4 × 10 m
= 40 m
Perimeter of the rectangular plot
40 = 2 (l + b) units
40 = 2 (l + 8) m
40 = 2 l + 16
2 l = 40 – 16
2 l = 24
l = \(\frac{24}{2}\)
l = 12 m
Area of the square plot
= a × a sq units
= 10 × 10 m²
= 100 m²
Area of the rectangular plot
= l × b sq units
= 8 × 12 m²
= 96 m²
Square plot has the greater area by 100 m² – 96 m² – 4 m²

Question 13.
Look at the picture of the house given and find the total area of the shaded portion.

Solution:
Total area of the shaded region = Area of a right triangle + Area of a rectangle
= (\(\frac{1}{2}\) × b × h) + (l × b) cm²
= [(\(\frac{1}{2}\) × 3 × 4) + (9 × 6)] cm²
= (6 + 54) cm² = 60 cm²

Question 14.
Find the approximate area of the flower in the given square grid.

Solution:
No of full squares = 11
No of half squares = 9
Area of 11 full squares
= 11 x 1 cm²
= 11 cm²
Area of 9 half squares
= 9 × \(\frac{1}{2}\) cm²
= 4.5 cm²
Area of the flower = (11 + 4.5) cm²
= 15.5 cm²

Students can download Maths Chapter 3 Perimeter and Area Ex 3.1 Questions and Answers, Notes, Samacheer Kalvi 6th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 3 Perimeter and Area Ex 3.1

Question 1.
The table given below contains some measures of the rectangle. Find the unknown values.

Solution:

(i) Area of the rectangle = (length × breadth) sq unit.
Perimeter of a rectangle = 2(1 + b) units.
l = 5 cm
b = 8 cm
∴ p = 2 (l + b) cm = 2 (5 + 8) cm = 2 × 13 cm
p = 26 cm
Area = (l × b) cm² = (5 × 8) cm²
A = 40 cm²

(ii) l = 13 cm
p = 54 cm
Perimeter = 2 (l + b) units
54 = 2 (13 + b) cm
\(\frac{54}{2}\) = 13 + b
27 = 13 + b
b = 27 – 13
b = 14 cm
Area = l × b sq. unit = 13 × 14 cm²
A = 182 cm²

(iii) b = 15 cm
p = 60 cm
p = 2 (l + b) units
60 = 2 (l + 15) cm
\(\frac{60}{2}\) = l + 15
30 = l + 15
l = 30 – 15 .
l = 15 cm
Area = l × b unit² = 15 × 15 cm² = 225 cm²
A = 225 cm²

(iv) l = 10 m
Area = 120 sq metre
Area = l × b sq.m
120 = 10 × 6
b = \(\frac{120}{10}\)
b = 12 m
Perimeter =2 (l + b) units = 2(10 + 12) units = 2 × 22 m
A = 44 m

(v) b = 4 feet.
Area = 20 sq. feet
Area = l × b sq .feet
20 = l × 4
l = \(\frac{20}{4}\) feet
l = 5 feet
Perimeter = 2 (l + b) units.
p = 2 (5 + 4) feet = 2 × 9
p = 18 feet

Question 2.
The table given below contains some measures of the square. Find the unknown values.

Solution:
(i) 24 cm, 36 cm²
(ii) 25 m, 625 m²
(iii) 7 feet, 28 feet

Question 3.
The table given below contains some measures of the right angled triangle. Find the unknown values.

Solution:

Area of the right triangle = \(\frac{1}{2}\) × (base × height) unit²
(i) b = 20 cm
h = 40 cm
Area = \(\frac{1}{2}\) (b × h) cm² = \(\frac{1}{2}\) × 20 × 40 = 400 cm²
A = 400 cm²

(ii) b = 5 feet
Area = \(\frac{1}{2}\) × b × h unit²
= 20 = \(\frac{1}{2}\) × 5 × h sq. feet
\(\frac{20 \times 2}{5}\) = h
h = 8 feet

(iii) Area = \(\frac{1}{2}\) × (base × height) unit²
24 = \(\frac{1}{2}\) × b × 12 m²
base = \(\frac{24 \times 2}{12}\) m = 4 m
Base = 4m

Question 4.
The table given below contains some measures of the triangle. Find the unknown values.

Solution:
(i) 13 cm
(ii) 6 m
(iii) 8 feet

Question 5.
Fill in the blanks.
(i) 5 cm² = ______ mm²
(ii) 26 m² = ______ cm²
(iii) 8 km² = ______ m²
Solution:
(i) 500
(ii) 260000
(iii) 8000000

Question 6.
Find the perimeter and area of the following shapes.

Solution:
(i) Perimeter = (4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4)
= 48 cm
a = 4 cm
Area of 1 square = 4 × 4 cm²
= 16 cm²
Area of 5 squares = 5 × 16 cm²
= 80 cm²

(ii) Perimeter = (4 + 5 + 4 + 5 + 4 + 5 + 4 + 5)
= 36 cm
Area of 1 triangle = \(\frac{1}{2}\) × b × h sq units
= \(\frac{1}{2}\) × 4 × 5 cm²
= 10 cm²
Area of 4 triangles= 4 × 10 cm²
= 40 cm²
Area of the square = 3 × 3 cm²
= 9 cm²
Total area = (40 + 9) cm²
= 49 cm²

(iii) Perimeter = (15 + 50 + 12 + 13 + 10 + 10 + 40)
= 150 cm
Area of the square = 10 × 10 cm²
= 100 cm²
= 250 cm²
Area of the triangle = \(\frac{1}{2}\) × 12 × 5 cm²
= \(\frac{1}{2}\) × 12⁶ x 5 cm²
= 30 cm²
Total area = (100 + 250 + 30) cm²
= 380 cm²

Question 7.
Find the perimeter and the area of the rectangle whose length is 6 m and breadth is 4m?
Solution:
l = 6 m, b = 4 m Perimeter of the rectangle
= 2 (l + b) units
= 2 (6 + 4) m
= 2 (10) m
= 20 m
Area of the rectangle = l × b sq units
= 4 × 6 m²
= 24 m²

Question 8.
Find the perimeter and area of a square whose side is 8 cm.
Solution:
a = 8 cm
The perimeter of a square
= 4a units
= 4 × 8 cm
= 32 cm
Area of the square = a × a sq units
= 8 × 8 cm²
= 64 cm²

Question 9.
Find the perimeter and the area of right angled triangle whose sides are 6 feet, 8 feet and 10 feet.
Solution:
Perimeter of the triangle
= (a + b + c) units
= (6 + 8 + 10) feet
= 24 feet
Area of the triangle = \(\frac{1}{2}\) × b × h sq units
\(\frac{1}{2}\) × 6³× 8 feet square = 24 sq. feet

Question 10.
Find the perimeter of
(i) A scalene triangle with sides 7 m, 8 m, 10 m.
(ii) An isosceles triangle with equal sides 10 cm each and third side is 7 cm.
(iii) An equilateral triangle with a side of 6 cm.
Solution:
(i) Perimeter of the triangle
= (a + b + c) units
= (7 + 8 + 10) m
= 25

(ii) Perimeter of the triangle
= (10 + 10 + 7) cm
= 27 cm

(iii) Perimeter of the triangle
= (6 + 6 + 6) cm
= 18 cm

Question 11.
The area of a rectangular shaped photo is 820 sq. cm. and its width is 20 cm. What is its length? Also find its perimeter.
Solution:
Given Area = 820 cm²
Width = 20 cm
Area of the rectangle
= l × b sq. units
820 = l × 20
\(\frac{820}{20}\) = l
41 = l
length l = 41 cm
Perimeter = 2(l + b) units
= 2(41 + 20) cm
= 2(61) cm
= 122 cm

Question 12.
A square park has 40 m as its perimeter. What is the length of its side? Also find its area.
Solution:
perimeter = 40 m
4a = 40 m
a = \(\frac{40}{4}\)
Side a = 10 m
Area = a × a sq units
= 10 × 10 m²
= 100 m²

Question 13.
The scalene triangle has 40 cm as its perimeter and whose two sides are 13 cm and 15 cm, find the third side.
Solution:
Let the third side be C
perimeter = (a + b + c) units
40 = 13 + 15 + C
40 = 28 + C
C = 40 – 28
C = 12 units
C = 12 cm

Question 14.
A field is in the shape of a right angled triangle whose base is 25 m and height 20 m. Find the cost of levelling the field at the rate of Rs 45/- per sq.m²
Solution:
b = 25 m, h = 20 m
Area of the triangle = \(\frac{1}{2}\) × bh sq.units
= \(\frac{1}{2}\) × 25 × 20 m²
= 250 m²
Cost of levelling 1 m² = Rs 45
Cost of levelling 250 m² = Rs 45 × 250
= Rs. 11250

Question 15.
A square of side 2 cm is joined with a rectangle of length 15 cm and breadth 10 cm. Find the perimeter of the combined shape.
Solution:

Perimeter of the combined shape = Lengths of the outer boundaries
= (15 + 10 + 2 + 2 + 2 + 13 + 10) cm = 54 cm
Perimeter = 54 cm

Objective Type Questions

Question 16.
The following figures are of equal area. Which figure has the least perimeter?

Solution:
(b)

Question 17.
If two identical rectangles of perimeter 30 cm are joined together, then the perimeter of the new shape will be
(a) equal to 60 cm
(b) less than 60 cm
(c) greater than 60 cm
(d) equal to 45 cm
Solution:
(b) less than 60 cm

Question 18.
If every side of a rectangle is doubled, then its area becomes _____ times
(a) 2
(b) 3
(c) 4
(d) 6
Solution:
(c) 4
2l × 2b = 4l × b

Question 19.
The side of the square is 10 cm. If its side is tripled, then by how many times will its perimeter increase?
(a) 2 times
(b) 4 times
(c) 6 times
(d) 3 times
Solution:
(d) 3 times

Question 20.
The length and breadth of a rectangular sheet of paper are 15 cm and 12 cm respectively. A rectangular piece is cut from one of its corners. Which of the following statement is correct for the remaining sheet?
(a) Perimeter remains the same but the area changes
(b) Area remains the same but the perimeter changes
(c) There will be a change in both area and perimeter
(d) Both the area and perimeter remains the same.
Solution:
(a) Perimeter remains the same but the area changes