Question

Find the area of the shaded portion in the given figure, where $ABCD$ is a square of side $14cm$ and semicircles are drawn with each side of square as diameter.

Answer 1

$AB=1$ & $\Rightarrow =\frac{14}{2}=7$

radius of semi circle $=\frac{14}{2}=7$

Since the diagram is stmmetric we could $k$ are of petal and multiply it by $4$

$4\times$(area of $1$ petal) $=$ area of $4$ petal

Area of $1$ petal:

area of shaded region in $\left(2\right)$

$=\frac{1}{2}$ (area of semi circle)

$=\frac{1}{2}\left[\frac{\pi r^2}{\alpha }\right]=\frac{\pi (r{)}^2}{4}=\frac{49\pi }{4}$

area of shaded region in $\left(3\right)$

$\Rightarrow 1/2\times bax\times height$

$\Rightarrow 1/2\times AP\times OP\Rightarrow 1/2\times 7\times 7\Rightarrow \frac{49}{2}$

$\therefore$ area of $\left(1\right)=area\left(2\right)-area\left)3\right)$

$=\frac{49\pi }{4}-\frac{49}{2}=\frac{49}{2}[\frac{\pi }{2}-1]$

area of $1$ petal $=2\times$area of $\left(1\right)$

area of petal $=2\times \frac{49}{2}[\frac{\pi }{2}-1]$

$\therefore$ area of shaded region $=4\times$area of $1$ petal $=4\times 49[\frac{\pi }{2}-1]$

area of shaded region $=196[\frac{\pi }{2}-1]$