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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.
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Solution
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
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