Question

The figure shows two paths drawn inside a rectangular field 60 m long and 30 m wide. If the width of each path is 5 m, then find the perimeter of the shaded portion.

Answer 1

Let's find the perimeter of the boundary line of the shaded portion in green by two methods:

Method-I

Perimeter of shaded portion = (Perimeter of the rectangle EFGH) + (Perimeter of the rectangle IJKL) - (Perimeter of the square MNOP)

= (2 (60 + 5)) + (2 (30 + 5)) - (4 × 5)

= 130 + 70 - 20

= 180 m.

Method - II

Perimeter of the shaded portion
= EM + MI + IJ + JN + NH + HG + GO + OK + KL + LP + PF + FE

= 27.5 + 12.5 + 5 + 12.5 + 27.5 + 5 + 27.5 + 12.5 + 5 + 12.5 + 27.5 + 5

= 180 m.

Therefore the perimeter of the boundary line of the shaded portion is 180 m.