Teachers can assign these Ganita Prakash Class 6 Worksheet and Class 6 Maths Chapter 6 Perimeter and Area Worksheet with Answers Pdf Download for daily practice.
Class 6 Maths Chapter 6 Perimeter and Area Worksheet with Answers Pdf
Perimeter and Area Class 6 Maths Worksheet
Class 6 Maths Chapter 6 Worksheet with Answers – Class 6 Perimeter and Area Worksheet
Multiple Choice Questions
1. Shawn travels 4 rounds of a square park of side 40 m. The distance travelled by Shawn is
(a) 160 m
(b) 240 m
(c) 640 m
(d) 480 m
Answer:
(c) 640 m
2. The length and breadth of a rectangle are 40 cm and 10 cm, respectively. Its perimeter is
(a) 100 cm
(b) 120 cm
(c) 140 cm
(d) 280 cm
Answer:
(a) 100 cm
3. The perimeter of a triangle whose sides are 5 cm, 2 cm and 3 cm is
(a) 10 cm
(b) 17 cm
(c) 11 cm
(d) 30 cm
Answer:
(a) 10 cm
4. To find the perimeter of the square floor of your classroom, we will
(a) add the length of sides.
(b) subtract the length of sides.
(c) multiply the length of sides.
(d) None of these
Answer:
(a) add the length of sides.
5. If the perimeter of a square garden is 444 m. Then, its side measures
(a) 101 m
(b) 111 cm
(c) 101 cm
(d) 111 m
Answer:
(d) 111 m
6. The perimeter of an isosceles triangle with equal sides of length 4 cm and third side of length 6 cm will be
(a) 10 cm
(b) 8 cm
(c) 20 cm
(d) 14 cm
Answer:
(d) 14 cm
7. The side of a square is 6 cm. If its side is doubled, then its new perimeter will be
(a) 64 cm
(b) 48 cm
(c) 44 cm
(d) 56 cm
Answer:
(b) 48 cm
7. If perimeter of an equilateral triangle is 36 cm. Then the length of each side is
(a) 6 cm
(b) 12 cm
(c) 8 cm
(d) 9 cm
Answer:
(b) 12 cm
8. Two regular pentagons of side 5 cm are joined together as shown in the figure. Find the perimeter of the new figure.
(a) 35 cm
(b) 40 cm
(c) 45 cm
(d) 50 cm
Answer:
(b) 40 cm
9. In the given rectangle MNOP, if the length is decreased by 3x, then the new perimeter will be
(a) (32x – 2) units
(b) (30x – 2) units
(c) (26x – 2) units
(d) (28x – 2) units
Answer:
(c) (26x – 2) units
10. The given figure is made up of one big square of side 5 cm and 3 identical small squares of side X cm each. The perimeter of the figure in terms of X is
(a) [20 + 6x] cm
(b) [20 + 5x] cm
(c) [18 + 7x] cm
(d) [20 + 9x] cm
Answer:
(a) [20 + 6x] cm
11. Which figure encloses more area: a square of side 2 cm or a rectangle of side lengths 3 cm and 2 cm?
(a) Square
(b) Rectangle
(c) Both have equal areas
(d) None of these
Answer:
(b) Rectangle
12. The area of a rectangle is 40 cm2. If its breadth is 4 cm, then its length is
(a) 20 cm
(b) 30 cm
(c) 10 cm
(d) 15 cm
Answer:
(c) 10 cm
13. A marble floor is covered with 25 square marbles of equal size. The side of the square marble is 3 cm. The area of the floor is
(a) 300 cm2
(b) 275 cm2
(c) 225 cm2
(d) 195 cm2
Answer:
(c) 225 cm2
14. The number of postal stamps that can be made out of a sheet of (384 × 172)cm2 paper, if each stamp requires a piece of paper of size (16 × 12) cm2, is
(a) 342
(b) 338
(c) 344
(d) 340
Answer:
(c) 344
15. A room is 5 m 40 cm long and 3 m 75 cm wide. The area of the carpet needed to cover the floor is
(a) 30 m2
(b) 27.5 m2
(c) 20.25 m2
(d) 19.5 m2
Answer:
(c) 20.25 m2
16. If the area of a square is 10000 m2. Then, its side measures
(a) 10 m
(b) 100 m
(c) 2000 m
(d) 15 m
Answer:
(b) 100 m
17. The area is expressed in the following units.
(a) unit
(b) square units
(c) cube units
(d) None of these
Answer:
(b) square units
18. Area of rectangular garden of 50 m broad is 300 m2, the length of garden is
(a) 6 cm
(b) 6 m
(c) 150 m
(d) 12 m
Answer:
(b) 6 m
19. If the area of one file is 10m2, then the area of 5 files will be
(a) 2 m2
(b) 50 m2
(c) 50 m2
(d) 11 m2
Answer:
(c) 50 m2
20. If the cost of filing a rectangular plot of area 100 m2 is ₹ 6, then the cost of filing the rectangular plot of area 800 m2.
(a) ₹ 48
(b) ₹ 24
(c) ₹ 12
(d) ₹ 96
Answer:
(a) ₹ 48
21. If the area of a rectangle is equal to the area of a square (of each side length S) and the length of the rectangle is equal to the perimeter of the square, then the breadth of the rectangle is
(a) \(\frac{S}{2}\)
(b) \(\frac{S^2}{2}\)
(c) \(\frac{S}{4}\)
(d) \(\frac{S}{3}\)
Answer:
(c) \(\frac{S}{4}\)
22. If the length of rectangle is two times the breadth and the area is 288 cm2, then the length and breadth of the rectangle respectively, are
(a) 20 cm, 10 cm
(b) 12 cm, 24 cm
(c) 24 cm, 12 cm
(d) 16 cm, 8 cm
Answer:
(c) 24 cm, 12 cm
23. A rectangular plot of land, whose length and breadth are 154 m and 65 m respectively, then its area and perimeter are, respectively
(a) 10010 m2, 438 m
(b) 100 m2, 44.4 m
(c) 10210 m2, 425 m
(d) 99.28 m2, 4.45 m
Answer:
(a) 10010 m2, 438 m
24. How many envelopes can be made out of a sheet of paper 72 cm by 48 cm, if each envelope requires a paper of size 18 cm by 12 cm ?
(a) 4
(b) 8
(c) 12
(d) 16
Answer:
(d) 16
25. The area of the shaded region in the given figure is
(a) 45 m
(b) 89 m2
(c) 90 m2
(d) 2000 m2
Answer:
(b) 89 m2
26. All the given figures consist of the same four squares of equal size. Which figure has the smallest perimeter?
Answer:
(a)
Assertion (A) and Reason (R)
Study the Assertion (A) and Reason (R) statements given below and choose the correct alternative.
1. Assertion (A) Breadth of the rectangle whose perimeter 160 cm and length 16 cm are 10 cm.
Reason (R) Perimeter of rectangle = 2 (Length + Breadth)
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(d) A is false but R is true.
2. Assertion (A) Perimeter of a regular hexagon with all each side length 7 cm is 42 cm.
Reason (R) Perimeter of n-sided regular polygon = n x [Length of one side]
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(a) Both A and R are true and R is the correct explanation of A.
3. Assertion (A) If a square, a rectangle and a triangle are all made from a string of length 30 cm, their perimeters will be same.
Reason (R) Sides of square, rectangle and triangle are of same length.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(c) A is true but R is false.
4. Assertion (A) A piece of a string is 30 cm long. If the string is used to form an equilateral triangle, then the length of each side will be 10 cm.
Reason (R) Perimeter of equilateral triangle = 3 x (side).
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(a) Both A and R are true and R is the correct explanation of A.
5. Assertion (A) The cost of fencing a rectangular park of length 200 m and breadth 50 m at the rate of ? 15 per meter is 17000.
Reason (R) Perimeter of rectangle = 2 x (length + breadth)
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(d) A is false but R is true.
6. Assertion (A) Area of rectangle = Length + Breadth
Reason (R) The amount of surface enclosed by a closed figure is called its area.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(d) A is false but R is true.
7. Assertion (A) A page is 25 cm long and 20 cm wide. The area of this page is 90 cm.
Reason (R) The amount of surface enclosed by a closed figure is called its area.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(C) A is true but R is false.
(d) A is false but R is true.
Answer:
(d) A is false but R is true.
8. Assertion (A) The length of rectangle of area 135 cm2 and breadth 9 cm is 15 cm.
Reason (R) Length of rectangle = Area × Breadth.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(c) A is true but R is false.
9. Assertion (A) Side of the square whose area is 225 sq m, is 15 m. Reason (R) The standard unit of area is sq units.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Answer:
(b) Both A and R are true but R is not the correct explanation of A.
Fill in the Blanks
1. Perimeter of a triangle is the sum of the lengths of __________ sides.
Answer:
3
2. If the perimeter of a square field is 16 m, then the length of a side of the field is __________ m.
Answer:
4
3. A triangle having a perimeter of 60 cm has three sides of length 15 cm, 19 cm and __________ cm.
Answer:
26
4. The perimeter of a rectangular blackboard having side lengths 6 m and 4 m is __________ m.
Answer:
20
5. A wire of length 30 cm is used to form a pentagon (a five-sided closed figure) with sides of equal length. The length of each side is __________ cm.
Answer:
6
6. The area of a rectangle is 20 cm2. If the breadth is 4 cm, then its length is ___________.
Answer:
5 cm
7. If each side of a square is halved, then its area will become ___________ .
Answer:
One-fourth
8. A square with the area of 144 cm2 has each side length equal to ___________ cm.
Answer:
12
9. If the area of one rectangular box is 50 m2 the area of 10 boxes will be ___________ m2.
Answer:
500
10. A table top measures 3 m by 50 cm, the area will be ___________ m2.
Answer:
1.5
True or False
State whether the following statements are True or False.
1. The distance covered along the boundary of a rectangle is called its perimeter.
Answer:
True
2. A man running around a square field of side 13.5 m covers a distance of 27 cm.
Answer:
False
3. Two squares of side 4 cm are joined together side by side to make a new figure which is a rectangle having side lengths 8 cm and 4 cm.
Answer:
True
4. The perimeter of an equilateral triangle is three times the length of its side.
Answer:
True
5. If the perimeter of a square is 160 m, then its side is 44 m.
Answer:
False
6. If the the side of a square is halved, then the new perimeter is two times the original perimeter.
Answer:
False
7. Area of a square is doubled if the side of the square is doubled.
Answer:
False
8. If the side of a square floor is 9 m, then the area of the carpet needed to cover the floor of the room is 36 m2.
Answer:
False
9. If the length of a rectangle is halved and breadth is doubled, then the area of the rectangle obtained remains same.
Answer:
True
10. Standard unit of area is square units.
Answer:
True
Match The Following
Question 1.
| Column A | Column B |
| (i) Reno runs around a square field of side 80 m. Dino runs around a rectangular field with length 170 m and breadth 110 m. What is the difference in the distances covered by Reno and Dino? | (a) 20 cm |
| (ii) Find the cost of fencing a rectangular park of length 260 m and breadth 180 m at the rate of? 12 per meter? | (b) 18 cm |
| (iii) A piece of string is 80 cm. What will be the length of each side if the string is used to form a square? | (c) 10560 |
| (iv) Four equilateral triangles of side 4.5 cm are joined together to make a new figure. Find the perimeter of the new figure? | (d) 240 |
Answer:
| Column A | Column B |
| (i) Reno runs around a square field of side 80 m. Dino runs around a rectangular field with length 170 m and breadth 110 m. What is the difference in the distances covered by Reno and Dino? | (c) 10560 |
| (ii) Find the cost of fencing a rectangular park of length 260 m and breadth 180 m at the rate of? 12 per meter? | (d) 240 |
| (iii) A piece of string is 80 cm. What will be the length of each side if the string is used to form a square? | (b) 18 cm |
| (iv) Four equilateral triangles of side 4.5 cm are joined together to make a new figure. Find the perimeter of the new figure? | (a) 20 cm |
Question 2.
| Column A | Column B |
| (i) If a rectangular plot of land is 400 m long and 300 m wide, then the total cost of tiling at the rate of 6 per hundred square metre is equal to? | (a) 28 m2 |
| (ii) If a room is 8 m long and 3 m 50 cm wide, then the area of carpet needed to cover the floor of the room is | (b) 90 m2 |
| (iii) A floor is 8 m long and 4 m wide. A square carpet of side 3 m is laid on the floor, then the area of the floor that is not carpeted is equal to | (c) 7200 |
| (iv) Ten square flower beds each of sides 3 m are dug on a piece of land 18 m long and 10 m wide, then the remaining part of the land is | (d) 30.25 cm2 |
| (v) Area of a square with side 5.5 cm is | (e) 23 m2 |
Answer:
| Column A | Column B |
| (i) If a rectangular plot of land is 400 m long and 300 m wide, then the total cost of tiling at the rate of 6 per hundred square metre is equal to? | (b) 90 m2 |
| (ii) If a room is 8 m long and 3 m 50 cm wide, then the area of carpet needed to cover the floor of the room is | (d) 30.25 cm2 |
| (iii) A floor is 8 m long and 4 m wide. A square carpet of side 3 m is laid on the floor, then the area of the floor that is not carpeted is equal to | (a) 28 m2
|
| (iv) Ten square flower beds each of sides 3 m are dug on a piece of land 18 m long and 10 m wide, then the remaining part of the land is | (e) 23 m2 |
| (v) Area of a square with side 5.5 cm is | (c) 7200 |
Complete the following tables.
Question 1.
(i) For a square
| Side | Perimeter |
| (a) 120 cm | __________ |
| (b) __________ | 400 cm |
| (c) 28 cm | __________ |
| (d) __________ | 248 cm |
| (e) 99 cm | __________ |
Answer:
(a) 480 cm
(b) 100 cm
(c) 112 cm
(d) 62 cm
(e) 396 cm
(ii) For a rectangle
| Length | Breadth | Perimeter |
| (a) 25 cm | 10 cm | _________ |
| (b) ______ | 65 cm | 770 cm |
| (c) 52 cm | ______ | 164 cm |
| (d) 135 cm | 71 cm | _________ |
| (e) _______ | 150 cm | 432 cm |
Answer:
(a) 70 cm
(b) 320 cm
(c) 30 cm
(d) 62 cm
(e) 432 cm
(iii) For a triangle
| Side 1 | Side 2 | Side 3 | Perimeter |
| (a) 15 cm | 10 cm | 7 cm | _________ |
| (b) ______ | 5 cm | 9 cm | 24 cm |
| (c) 22 cm | ________ | 8 cm | 42 cm |
| (d) 35 cm | 7 cm | ________ | 54 cm |
| (e) 200 cm | 150 cm | 82 cm | _________ |
Answer:
(a) 32 cm
(b) 10 cm
(c) 12 cm
(d) 2 cm
(e) 432 cm
(iv) Calculate the perimeter of the following figures.
Answer:
(a) 495 cm
(b) 72 cm
(c) 72 cm
(d) 28 cm
(e) 34 cm
Question 2.
Find the area by counting the number of squares in the given figures (asume 1 square = 1 sq unit) and complete the table given below.
Answer:
(i) 2 sq. units
(ii) 5 sq. units
(iii) 12 sq. units
(iv) 10 sq. units
(v) 4 sq. units
Very Short Answer Type Questions
Question 1.
Find the missing length of the given figure.
______________________________________
Answer:
6 cm
Question 2.
Find the perimeter of an isosceles triangle with equal sides 8.5 cm each and third side 7 cm.
______________________________________
Answer:
24 cm
Question 3.
Find the area of a square piece of card board with side 6 cm.
______________________________________
Answer:
36 cm2
Question 4.
Find the perimeter of the given figure?
______________________________________
Answer:
34 cm
Question 5.
The perimeter of a regular hexagon is 36 cm, then find the length of each side.
______________________________________
Answer:
6 cm
Question 6.
The perimeter of a rectangle is 82 cm. If the length of the rectangle is 30 cm, find its breadth.
______________________________________
Answer:
11 cm
Question 7.
The perimeter of a regular pentagon is 80 cm. How long is its each side.
______________________________________
Answer:
16 cm
Question 8.
The area of a rectangle is 240 cm2. If its length is 20 cm, then find its breadth.
______________________________________
Answer:
12 cm
Question 9.
Find the area of the given figure.
______________________________________
Answer:
25 cm2
Question 10.
The perimeter of regular octagon is 120 cm. How long is its each side?
______________________________________
Answer:
15 cm
Short Answer Type Questions
Question 1.
Find the area of the shaded region in the given figure.
______________________________________
______________________________________
Answer:
17 cm2
Question 2.
The area of a rectangle is 630 cm2 and its length is 35 cm. Find the perimeter of the rectangle.
______________________________________
______________________________________
Answer:
106 cm
Question 3.
The length of a rectangular field is four times its breadth. If the perimeter of this field is 800 m, then what is the length of the field?
______________________________________
______________________________________
Answer:
320 m
Question 4.
Find the area of the given figures, by splitting them into rectangles.
Answer:
(a) 26 m2
(b) 43.5 m2
(c) 33 m2
(d) 9 cm2
Question 5.
There is a rectangular lawn 10 m long and 4 m wide in front of Meena’s house. It is fenced along the two smaller sides and one longer side leaving a gap of 1 m for the entrance. Find the length of fencing.
______________________________________
______________________________________
Answer:
17 m
Question 6.
The total cost of flooring a room at ₹ 7.50 per sq m is ₹ 450. If the length of room is 8 m, then find its breadth.
______________________________________
Answer:
7.5 m
Question 7.
The floor of a rectangular hall is to be covered with a carpet. If the length and breadth of the hall are 20 m and 18 m, respectively. Find the cost of the carpet at the rate of ₹ 10 per sq m.
______________________________________
Answer:
₹ 3600
Long Answer Type Questions
Question 1.
In the given figure, all triangles are equilateral and AB = 8 units. Other triangles have been formed by taking the mid-points of the sides. What is the perimeter of the figure?
______________________________________
______________________________________
______________________________________
Answer:
45 cm
Question 2.
The cost of fencing a square field at ₹ 16 per m is ₹ 32000. Find the cost of reaping the field at ₹ 35 per 100 m2.
______________________________________
______________________________________
______________________________________
Answer:
₹ 87500
Question 3.
A plot is in the form of a rectangle. The length and the breadth of this rectangular plot is 150 m and 50 m, respectively. Owner of this plot wants an odd age home for elderly people as shown is figure.
(a) Find the area of this plot.
______________________________________
Answer:
7500 m2
(b) Which value are depicted here?
______________________________________
Answer:
Humanity, social cooperation, caring and helpfulness for others
Case-based Questions
Question 1.
Sam, Kim and Tom go daily on morning walk in the city park. The city park is a rectangular park which has the length X cm and the breadth Y cm. Due to the routine cleaning, the entry of park is not available for two days so that they decided to go another park which is a square park having the side Z cm.
Read the passage carefully and answer the questions based on it.
(i) If X is greater than Y and Y is greater than Z, then which is correct in greater area?
(a) Square park
(b) Rectangular park
(c) Both are equal.
(d) None of these
Answer:
(b) Rectangular park
(ii) If X is greater than Y and Y is greater than Z, then which is correct perimeter?
(a) Square park has less perimeter than rectangular park.
(b) Rectangular park has less perimeter than square park.
(c) Both are equal.
(d) None of the above
Answer:
(a) Square park has less perimeter than rectangular park.
(iii) If the area of rectangular park is more than that of square park, what will be the difference of their areas?
(a) (X × Y) – (Z × Z)
(b) (Z × Z) – (X × Y)
(c) (Z × X) – (Z × Y)
(d) (Z × Y) – (X × Y)
Answer:
(a) (X × Y) – (Z × Z)
Activity
Activity 1
Solve the crossword puzzle and fill the given box across and down word as per the mentioned due in the boxes.
Across
2. The area of a ___________ is length x breadth.
3. The distance around the outside of a simple closed figure is called its ___________.
6. The shorter side of a rectangle is called its ___________.
8. A regular ___________ has five equal sides.
Down
1. A ___________ is a quadrilateral having all sides equal and its diagonal are equal.
4. A simple closed figure made of three line segments is called ___________.
5. The greater side of a rectangle is called its ___________.
7. The product of the length and breadth of a rectangle gives its ___________.
Answer:
1. Square
2. Rectangle
3. Perimeter
4. Triangle
5. Length
6. Breadth
7. Area
8. Pentagon
The post Perimeter and Area Class 6 Worksheet with Answers Maths Chapter 6 appeared first on Learn CBSE.
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