Question - 1 : - A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.

Answer - 1 : -

Given: Length = 90 m
Breadth = 75 m
Area of the garden = l × b
= 90 m × 75 m = 6750 m²
Length of the garden including path
= 90m + 5m + 5m = 100 m
Breadth of the garden including path
= 75m + 5m + 5m = 85m
Area of the garden including path
= l × b
= 100 m × 85 m = 8500 m²
Area of the path = 8500 m² –6750 m² = 1750 m²
Hence, required area of path = 1750 m² andarea of the garden = 6750 m² =0.675 ha

Question - 2 : - A 3 m wide path runs outside and around a rectangular park of length 125 m and breadth 65 m. Find the area of the path.

Answer - 2 : -

Length of the park = 125 m
Breadth of the park = 65 m
Area of the park = l × b
= 125 m × 65 m = 8125 m²

Length of the park including path
= 125 m + 3m + 3m = 131 m
Breadth of the park including path
= 65m + 3m + 3m = 71m
Area of the park including path
= 131 m × 71 m = 9301 m²
∴ Areaof the path
= 9301 m² – 8125 m² = 1176 m²
Hence, the required area = 1176 m².

Question - 3 : - A picture is painted on a cardboard 8 cm long and 5 cm wide such that there is a margin of 1. 5 cm along each of its sides. Find the total area of the margin.

Answer - 3 : -

Length = 8 cm, breadth = 5 cm
Area of the cardboard = l × b
= 8 cm × 5 cm = 40 cm²
Width of the margin = 1.5 cm
Length of the inner cardboard
= 8 cm – 1.5 × 2 cm
= 8 cm – 3 cm = 5 cm
Breadth of the inner cardboard
= 5 cm – 1.5 × 2 cm
= 5 cm – 3 cm = 2 cm
Area of the inner rectangle = l × b
= 5 cm × 2 cm = 10 cm² Area ofthe margin
= 40 cm² – 10 cm² = 30 cm²
Hence, the required area = 30 cm².

Question - 4 : -
A verandah of width 2.25 m is constructed all along outside a room which is 5.5 m long and 4 m wide. Find:
(i) the area of the verandah.
(ii) the cost of cementing the floor of the verandah at the rate of ₹ 200 per m2.

Answer - 4 : -

Length of the room = 5.5 m
Breadth of the room = 4 m
∴ Areaof the room = l × b = 5.5 m × 4 m = 22 m²
Width of the verandah = 2.25 m
Length of the room including verandah
= 5.5 m + 2 × 2.25 m = 10 m
Breadth of the room including verandah
= 4 m + 2 × 2.25 m = 8.50 m²
Area of the room including verandah = l × b
= 10 m × 8.50 m = 85 m²
(i) Area of the verandah = 85 m² –22 m²
= 63 m²
(ii) Cost of cementing the floor of the verandah = ₹ 63 × 200 = ₹12600

Question - 5 : - A path 1 m wide is built along the border and inside asquare garden of side 30 m. Find:
(i) the area of the path.
(ii) the cost of planting grass in the remaining portion of the garden at therate of ₹ 40 per m².

Answer - 5 : -

Area of the square garden = (Side)²
= 30 m × 30 m = 900 m²
Length of the garden excluding the path = 30 m – 2 × 1 m = 28 m
∴ Areaof the garden excluding the path = 28 m × 28 m = 784 m²
(i) Area of the path = 900 m² –784 m²
= 116 m²
(ii) Cost of the planting the remaining portion at the rate of ₹ 40 per m²
= ₹ 40 × 784 = ₹ 31,360

Question - 6 : - Two cross roads, each of width 10 m, cut a right angles through the centre of a rectangular park of length 700 m and breadth 300 m and parallel to its sides. Find the area of the roads. Also find the area of the park excluding cross roads. Give the answer in hectares.

Answer - 6 : -

Length of the road parallel to the length of the park = 700 m
Width of the road = 10 m
∴ Areaof the road = l × b = 700 m × 10 m = 7000 m²
Length of the road parallel to the breadth of the park = 300 m
Width of the road = 10 m Area of this road = l × b = 300 m × 10 = 3000 m²
Area of the both roads
= 7000 m² + 3000 m² – Area of the common portion
= 10,000 m² – 10 m × 10 m
= 10,000 m² – 100 m²
= 9900 m² = 0.99 ha
Area of the park = l × b
= 700 m × 300 m = 210000 m²
Area of the park excluding the roads
= 210000 m² – 9900 m²
= 200100 m² = 20.01 ha

Question - 7 : -
Through a rectangular field of length 90 m and breadth 60 m, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is 3 m, find
(i) the area covered by the roads.
(ii) the cost of constructing the roads at of the rate of ₹ 110 per m2.

Answer - 7 : -

Length of the road along the length of the field = 90 m
Breadth = 3 m
∴ Areaof this road = l × b
= 90 m × 3 m = 270 m²
Similarly, the area of the road parallel to the breadth of the field = l × b
= 60 m × 3 m = 180 m² Area ofthe common portion
= 3m × 3m = 9m²
(i) Area of the two roads
= 270 m² + 180 m² – 9 m²
= 450 m² – 9 m² = 441 m²
(ii) Cost of constructing the roads
= ₹ 110 × 441 = ₹ 48,510

Question - 8 : - Pragya wrapped a card around a circular pipe of radius 4 cm and cut off the length required of the cord. Then she wrapped it around a square box of side 4 cm (also shown). Did she have any cord left? (π = 3.14)

Answer - 8 : -

Length of the cord = Circumference of the circular pipe
= 2πr = 2 × 3.14 × 4 = 25.12 cm
Perimeter of the square box
= 4 × side = 4 × 4 cm = 16 cm
Length of the cord left
= 25.12 cm – 16 cm = 9.12 cm
Yes, 9.12 cm cord is left.

Question - 9 : -
The given figure represents a rectangular lawn with a circular flower bed in the middle. Find:
(i) the area of the whole land.
(ii) the area of the flower bed.
(iii) the area of the lawn excluding the area of the flower bed.
(iv) the circumference of the flower bed.

Answer - 9 : - (i) Length of the lawn = 10 m
Breadth of the lawn = 5 m
Area of the lawn = l × b
= 10 m × 5 m = 50 m²
(ii) Area of the circular flower bed = πr²
=(22/7)×2×2=(88/7)m²=12.57m²
(iii) Area ofthe lawn excluding the area of the flower bed

Question - 10 : - In the following figures, find the area of the shaded portion.

Answer - 10 : - (i) Area of the rectangle = l × b
= 18 cm × (6 cm + 4 cm)
= 18 cm × 10 cm = 180 cm²
Area of right triangle

Area of right ∆BCE = 12 ×b × h
= (1/2) ×8 × 10 =40 cm²
Area of the two right triangles
= 30 cm² + 40 cm² = 70 cm²
Area of the shaded portion
= 180 cm² – 70 cm² = 110 cm²
(ii) Area of the square PQRS = (Side)²
= (20)² = 400 cm²

Area ofthe three triangles
= 50 cm² + 100 cm² + 100 cm² =250 cm²
Area of the shaded portion
= 400 cm² – 250 cm² = 150 cm²

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