Question

The diagram, given below, shows two paths drawn inside a rectangular field 80 m long and 45 m wide. The widths of the two paths are 8 m and 15 m as shown. Find the area of the shaded portion. 

Answer 1

Consider the following figure.

Thus, the area of the shaded portion

= Area( ABCD ) + Area( EFGH ) - Area( IJKL )           …(1)

Dimensions of ABCD: 45m × 15 m

Thus, the area of ABCD = 45 × 15 = 675 m²

Dimensions of EFGH: 80 m × 8 m

Thus, the area of EFGH = 80 × 8 = 640m²

Dimensions of IJKL: 15 m × 8 m

Thus, the area of IJKL = 15 × 8 = 120 m²

Therefore, from equation (1),

the area of the shaded portion = 675 + 640 - 120 = 1195 m²