Question

Find the area of the shaded region in Figure, where arcs drawn with centres $A,B,C$ and $D$ intersect in pairs at mid-point $P,Q,R$ and $S$ of the sides $AB,BC,CD$ and $DA$ respectively of a square $ABCD$ of side $12cm$ [Use $\pi =3.14$].

Answer 1

Given side of the square $BC=12cm$

Since, $Q$ is the midpoint of $BC$

Radius $=BQ=\frac{12}{2}=6cm$

Area of quadrant $BPQ=\frac{\pi r^2}{4}=\frac{6^2\pi }{4}=\frac{113.04}{4}c{m}^2$

Area of four quadrants $=4\times \frac{113.04}{4}=113.04c{m}^2$

Area of square $={12}^2=144c{m}^2$

$\therefore$ Area of shaded region $=$ Area of square $-$ Area of four quadrants

$=144-113.04$

$\therefore$ Area of shaded region $=30.96c{m}^2$