A rectangulr field is 50 m by 40 m. It has two roads through its centre, running parallel to its sides. The width of the longer and shorter roads are 1.8 m and 2.5 m respectively. Find the area of the roads and the erea of the remaining portion of the field.

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Solution

Let ABCD be the rectangular field and KLMN and PQRS the two rectangular roads with width 1.8 m and 2.5 m, respectively.

Length of the rectangular field CD = 50 cm and breadth of the rectangular field BC = 40 m
∴ Area of the rectangular field ABCD = 50 m x 40 m = 2000 m²
Area of the road KLMN = 40 m x 2.5 m = 100 m²
Area of the road PQRS = 50 m x 1.8 m = 90 m²
Clearly area of EFGH is common to the two roads.
Thus, Area of EFGH = 2.5 m x 1.8 m = 4.5 m²
Hence,
Area of the roads = Area (KLMN) + Area (PQRS) − Area (EFGH)
= (100 m² + 90 m²) − 4.5 m² = 185.5 m²

Area of the remaining portion of the field = Area of the rectangular field ABCD − Area of the roads
= (2000 − 185.5) m²
= 1814.5 m²

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