Question

The given figure represents a kite with a circular and a semicircular motifs stuck on it. The radius of circle is $2.5cm$ and the semicircle is $2cm$. If diagonals $AC$ and $BD$ are the lengths $12cm$ and $8cm$ respectively, find the area of the unshaded part (in $c{m}^2$).

Answer 1

Let kite $ABCD$ be a quadrilateral.
$\therefore$ Area of quad. $=\frac{1}{2}\times$ the product of the diagonals
Area of kite $=\frac{1}{2}BD\times AC$
$=\frac{1}{2}\times 8\times 12$
$=48squarecm$.

Radius of circle $R=2.5cm$, Radius of semicircle $r=2cm$.
Area of shaded part $=$ Area of semicircle $+$ Area of circle
$=\frac{1}{2}\pi r^2+\pi R^2$
$=\frac{\pi (2{)}^2}{2}+\pi (2.5{)}^2$
$=2\pi +6.25\pi$
$=8.25\pi$
$=8.25\times \frac{22}{7}$
$=25.92\simeq 26c{m}^2$.

Area of unshaded part $=$ Area of kite $-$ Area of shaded part
$=48-26$
$=22c{m}^2$.