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

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Solution

We have,
Length of the rectangular field = 90 m and breadth of the rectangular field = 60 m

∴ 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

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