Question

If a circle is inscribed in a square of area $4$ sq units, then the area of the circle is

• A. $\pi$
• B. $\frac{\pi }{2}$
• C. `$\frac{\pi }{4}$
• D. $\frac{3\pi }{4}$

Answer 1

The correct option is A $\pi$

$\Rightarrow$ Area of a square $=4$ square units.

Let $a$ be side of square.

$\Rightarrow$ $a^2=4$

$\Rightarrow$ $a=2$ units.

Diameter of circle and side of square are equal.

$\therefore$ $r=\frac{2}{2}=1$ unit.

$\Rightarrow$ Area of a circle inscribed in a square $=\pi r^2$

$=\pi \times (1{)}^2$

$=\pi$