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.
Click here for the solutions of
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
