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A day full of math games & activities. Find one near you.

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 the rate of ₹ 110 per m2.

Solution:

Let's draw a figure according to the given question as shown below.

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 the rate of ₹ 110 per m2.

Let the blue region represent the rectangular field and the orange region represent the roads.

Length of the road along the length of the field = 90 m

Width of the road = 3 m

Area of the road ABDC = Length × Breadth

= 90 m × 3 m

= 270 m2

Length of the road parallel to the breadth of the field = 60 m

Width of the road = 3m

Area of the road EFGH = Length × Breadth

= 60 m × 3 m

= 180 m2

Note that IJLK  is a common region between the two roads which is a square with a side length of 3 m.

(i) Area of both the roads = Area of the road ABDC + Area of road EFGH - Area of Common Portion IJLK

= 270 m2 +180 m2 - (3 × 3) m2

= 450 m2 - 9 m2

= 441 m2

(ii) The cost of constructing 1 m2 road = Rs. 110

Cost of constructing 441 m2 road = Rs. 110 × 441

= Rs. 48,510

☛ Check: NCERT Solutions Class 7 Maths Chapter 11

Video Solution:

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 the rate of ₹ 110 per m².

Maths NCERT Solutions Class 7 Chapter 11 Exercise 11.4 Question 7

Summary:

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, then (i) the area covered by the roads is 441 m2, (ii) the cost of constructing the roads at the rate of ₹ 110 per m2 is ₹ 48,510.

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