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.

(i) Here, PQ = 3 m and PS = 60 m, EH = 3 m and
EF = 90 m and KL = 3 m and KN = 3 m
Area of roads = Area of PQRS + Area of EFGH – Area of KLMN
[∵ KLMN is taken twice, which is to be subtracted]
= PS x PQ + EF x EH – KL x KN
= (60 x 3) + (90 x 3) – (3 x 3)
= 180 + 270 – 9
= 441 m²
(ii) The cost of 1m² constructing the roads = ₹110
The cost of 441m² constructing the roads = ₹110 x 441 = ₹48,510
Therefore, the cost of constructing the roads = ₹48,510

Class 7 Maths Chapter 11 Exercise 11.4

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