# Mensuration

## Exercise 10.1

1). Find the perimeter of each of the following figures:

a). Perimeter = 4 + 2 + 4+ 2

= 12 cm

b). Perimeter = 23 + 35 + 40 + 35

= 133 cm

c). Perimeter = 15 + 15 + 15 + 15

= 60 cm

d). Perimeter = 4 + 4 + 4+ 4 + 4

= 20 cm

e). Perimeter = 1 + 4 + 0.5 + 2.5 + 2.5 + 0.5 + 4

= 15 cm

f). Perimeter = 1+3+2+3+4+1+3+2+3+4+1+3+2+3+4+1+3+2+3+4

= 4 X 1 + 4 X 2 + 8 X 3 + 4 X 4

= 4 + 8 + 24 + 16

= 52 cm

2). The lid of a rectangular box of sides 40 cm by 10 cm is sealed all around with tape. What is the length of the tape required?

Given: length of the rectangular box = 40 cm

breadth of the rectangular box = 10 c

perimeter of the rectangular box = 2 (length + breadth)

= 2 (40 + 10)

= 2 (50)

= 100 cm

Ans: length of the tape required = 100 cm.

3). A table-top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table-top?

Given: length of the table top = 2 m 25 cm = 2.25 m

breadth of the table top = 1m 50 cm = 1.50 m

perimeter of the rectangular box = 2 (length + breadth)

= 2 (2.25 + 1.50)

= 2 (3.75)

= 7.50 cm

Ans: perimeter of the table top = 7 m 50 cm

4). What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?

Given: length of the wooden strip = 32 cm

breadth of the wooden strip = 21 cm

perimeter of the wooden strip = 2 (length + breadth)

= 2 (32 + 21)

= 2 (53)

= 106 cm

Ans: length of the wooden strip =106 cm

5). A rectangular piece of land measures 0.7 km by 0.5 km. Each side is to be fenced with 4 rows of wires. What is the length of the wire needed?

Given: length of the land = 0.7 km

breadth of the land = 0.5 km

number of rows = 4

perimeter of the land = 2 (length + breadth)

= 2 (0.7 + 0.5)

= 2 (1.2)

= 2.4 km

Fence of the land = perimeter of the land

4 rows of fence = 4 X perimeter of the land

= 4 X 2.4

= 9.6 km

Ans: length of the wire needed = 9.6 km

6). Find the perimeter of each of the following shapes :

(a) A triangle of sides 3 cm, 4 cm and 5 cm.

Perimeter of triangle = sum of the three sides

= 3 + 4 + 5

= 12 cm

Ans: Perimeter of the triangle = 12 cm

(b) An equilateral triangle of side 9 cm.

Perimeter of equilateral triangle = sum of the three sides

= 9 + 9 + 9

= 27 cm

Ans: Perimeter of the equilateral triangle = 27 cm

(c) An isosceles triangle with equal sides 8 cm each and third side 6 cm.

Perimeter of isosceles triangle = sum of the three sides

= 8 + 8 + 6

= 22 cm

Ans: Perimeter of the isosceles triangle = 22 cm

7). Find the perimeter of a triangle with sides measuring 10 cm, 14 cm and 15 cm.

Given: sides of the triangle are 10 cm, 14 cm and 15 cm

Perimeter of triangle = sum of the three sides

= 10 + 14 + 15

= 39 cm

Ans: Perimeter of the triangle = 39 cm

8). Find the perimeter of a regular hexagon with each side measuring 8 m.

Given: side of the regular hexagon = 8 m

perimeter of the regular hexagon = 6 X side

= 6 X 8

= 48 m

Ans: perimeter of the regular hexagon = 48 m

9). Find the side of the square whose perimeter is 20 m.

Given: perimeter of the square = 20 m

perimeter of the square = 4 X side

20 = 4 X side

4 X side = 20

Side = 20 ÷ 4

= 5

Ans: side of the square = 5 m

10). The perimeter of a regular pentagon is 100 cm. How long is its each side?

Given: perimeter of the regular pentagon = 100 m

Side of the regular pentagon = ?

perimeter of the regular hexagon = 5 X side

5 X side = 100

Side = 100 ÷ 5

= 20

Ans: side of the regular pentagon = 20 m

11). A piece of string is 30 cm long. What will be the length of each side if the string is used to form :

(a) a square?

Given: perimeter of the square = 30 cm

Side of the square = ?

perimeter of the square = 30 cm

4 X side = 30

Side = 30 ÷ 4

= 7.5 cm

Ans: side of the square = 7.5 m

(b) an equilateral triangle?

Given: perimeter of the equilateral triangle = 30 cm

Side of the equilateral triangle = ?

perimeter of the equilateral triangle = 3 X side

3 X side = 30

Side = 30 ÷ 3

= 10

Ans: side of the equilateral triangle = 10 cm

(c) a regular hexagon?

Given: perimeter of the regular hexagon = 30 cm

Side of the regular hexagon = ?

perimeter of the regular hexagon = 6 X side

6 X side = 30

Side = 30 ÷ 6

= 5

Ans: side of the regular hexagon = 5 cm

12). Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is its third side?

Given: Two sides of the triangle are 12 cm and 14 cm

perimeter of the triangle = 36 cm

third side = ?

perimeter of the triangle = sum of the three sides

36 = 12 + 14 + third side

36 = 26 + third side

26 + third side = 36

Third side = 36 – 26

Third side = 10 cm

Ans: third side = 10 cm

13). Find the cost of fencing a square park of side 250 m at the rate of ₹ 20 per metre.

Given: side of the square park = 250 m

rate of fencing = ₹ 20 per metre

cost of fencing = ?

perimeter of the square park = 4 X side

= 4 X 250

= 1000 m

cost of fencing = rate X perimeter

= 20 X 1000

= 20000

Ans: cost of fencing = ₹ 20000

14). Find the cost of fencing a rectangular park of length 175 m and breadth 125 m at the rate of ₹12 per metre.

Given: length of the rectangular park = 175 m

breadth of the rectangular park = 125 m

rate of fencing = ₹ 12 per metre

perimeter of the rectangular park = 2 (length + breadth)

= 2 (175 + 125)

= 2 (300)

= 600 m

cost of fencing = rate X perimeter

= 12 X 600

= 7200

Ans: cost of fencing = ₹ 7200

15). Sweety runs around a square park of side 75 m. Bulbul runs around a rectangular park with length 60 m and breadth 45 m. Who covers less distance?

Given: side of the square park = 75 m

length of the rectangular park = 60 m

breadth of the rectangular park = 45 m

perimeter of the square park = 4 X side

= 4 X 75

= 300 m

perimeter of the rectangular park = 2 (length + breadth)

= 2 (60 + 40)

= 2 (100)

= 200 m

200 < 300

Perimeter of square park < perimeter of rectangular park

Ans: Bulbul covers less distance.

16). What is the perimeter of each of the following figures? What do you infer from the answers?

a) perimeter = 4 X side

= 4 X 25

= 100 cm

b) perimeter of the rectangular box = 2 (length + breadth)

= 2 (30 + 20)

= 2 (50)

= 100 cm

c) perimeter of the rectangular box = 2 (length + breadth)

= 2 (40 + 10)

= 2 (50)

= 100 cm

d) perimeter of the triangle = sum of the three sides

= 30 + 30 + 40

= 100

Ans: perimeter of all the shapes is same.

17). Avneet buys 9 square paving slabs, each with a side of ½ m. He lays them in the form of a square.

(a) What is the perimeter of his arrangement [Fig 10.7(i)]?

Perimeter = sum of all the sides

= 1 ½ + 1 ½ + 1 ½ + 1 ½

= 6 m

(b) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement [(Fig 10.7 (ii)]?

Perimeter = sum of all the sides

= 1 +1 + ½ + 1 + 1 + ½ + 1 + 1 + ½ + 1 + 1 + ½

= 10 m

(c) Which has greater perimeter?

Ans: (Fig 10.7 (ii) has the greater perimeter.

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Chapter 10 Mensuration

Chapter 8 Decimals

Chapter 7 Fractions

Chapter 6 Integers

Chapter 5 Understanding Elementary Shapes

Chapter 4 Basic Geometrical Ideas

Chapter 3: Playing With Numbers

Chapter 2: Whole Numbers

Chapter 1: Knowing Our Numbers