Question

A square of area $40{cm}^2$ is inscribed in a semicircle as shown in figure. The area (in ${cm}^2$) of the semicircle is

• A. $40\pi$
• B. $30\pi$
• C. $25\pi$
• D. $20\pi$

Answer 1

Answer: (C)

$25\pi$

Let the side of the square is $a$.
Area of the square $=40$ (given)


The radius of the semicircle is dividing the side of the square into 2 equal halves.
Applying the Phythogarous Theorem,


$=\frac{5}{4}\times 40=5\times 10$

$r=5\sqrt{2}$
Area of semicircle =
$r=5\sqrt{2}$
So on putting value of $r$, area of semicircle is
Area $=25\pi$
Hence, the correct option is C.