Question

Through a rectangular field of sides 90 m x 60 m, two roads are constructed which are parallel to the sides and cut each other at right angles through the center of the field. If the width of the roads is 3 m, find the total area covered by the two roads.

Answer 1

Given length of rectangular field = 90m

Breadth of rectangular field = 60m

Area of the rectangular field = 90 m x 60 m = 5400 m²

Area of the road PQRS = 90 m x 3 m

= 270 m²

Area of the road ABCD = 60 m x 3 m

= 180 m²

Clearly, area of KLMN is common to the two roads.

Thus, area of KLMN = 3 m x 3 m

= 9 m²

Hence, area of the roads = Area (PQRS) + Area (ABCD) – Area (KLMN)

= (270 + 180) m² – 9 m² 

= 441 m²