Question

Question 119 (i)

A square tile of length 20 cm has four quarter circles at each corner as shown in the figure.
Find the area of shaded portion.

Answer 1

Area of shaded portion
= Area of square - $4\times$ Area of quarter circle
$=20\times 20-4\times \frac{\pi r^2}{4}$
[$\because$ area of square =$(side{)}^2$ and area of quarter circle $=\frac{1}{4}$ area of a circle]
$=400-4\times \frac{22}{7}\times \frac{1}{4}\times 10\times 10$ [$\because$ radius of quarter circle $=\frac{1}{2}$ side of square = 10 cm]
$=400-\frac{2200}{7}=\frac{600}{7}=85.71c{m}^2\approx 86c{m}^2$