Question

Find the perimeter and area of the shaded portion of the following diagram; give your answer correct to 3 significant figures. (Take π = 22/7).

Answer 1

Area of rectangle = 28 m x 26 m = 728 m²
(i) Perimeter of the shaded position 
= 2 x 28 + 2 x 26 - 4 x 20 + 2 x ${\displaystyle \frac{22}{7}}$ x 10

= 56 + 52 - 80 + ${\displaystyle \frac{440}{7}}$

= 108 - 80 + 62.85
= 170.85 - 80 
= 90.85 m.

(ii) Area of one corner (unshaded) = ${\displaystyle \frac{1}{4}}$ π x (10)²
= ${\displaystyle \frac{1}{4}}$ x (3.14)(100 m²) 

= ${\displaystyle \frac{314}{4}}$
= 78.5 m²
∴ Area of 4 corners (unshaded) = 78.5 x 4 = 314 m²
∴ Area of  the shaded portion = [728 - 314] m² = 414 m².