Question

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

Answer 1

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

Given that length of rectangular field = 50 m

Breadth of rectangular field = 40m

Area of 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 of KLMN + Area of PQRS – Area of 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