Question

$ABCD$ is diameter of a circle of radius $6cm$ such that $AB=BC=CD$. Semicircles are drawn on $AB$ and $BD$ as diameter, as shown in the given figure. Find the area of the shaded region.

Answer 1

Since, Length of AB, BC and CD are equal.

Radius of circle $=6$cm

Now, AD$=2\times 6=12$cm

$\Rightarrow AB+BC+CD=12$

$\Rightarrow 3AB=12$

$\Rightarrow AB=\frac{12}{3}$

$\Rightarrow AB=4$cm

$\Rightarrow AB=BC=CD=4$cm

Radius of semicircle AB$=2$cm

Radius of semicircle BC$=4$cm

Radius of semicircle AD$=6$cm

Area of the shaded region $=$ Area of semicircle (AB$+$AD) $-$ Area of semicircle (BD)

$\Rightarrow$ Area of shaded region $=0.5\pi (2^2+6^2)-0.5\pi (4{)}^2$

$\Rightarrow$ Area of shaded region $=0.6\pi (4+36)-0.5\pi \times 16$

$\Rightarrow$ Area of shaded region $=20\pi -8\pi$

$\Rightarrow$ Area of shaded region $=12\pi c{m}^2$.