Question

Find the area of shaded portion of the given figure.

• A. $a^2-2\pi a^2$
• B. $2a^2-\frac{\pi a^2}{2}$
  
• C. $a^2-\frac{\pi a^2}{4}$
  
• D. $a^2-2\pi a^2$

Answer 1

The correct option is C $a^2-\frac{\pi a^2}{4}$


As we can see the figure given in the question is a circle inscribed in a square.
So for the area of the shaded region, we have to subtract the area of the circle from area of square.

Area of the square = $(side{)}^2=a^2$

Here we know the diameter of the circle from given figure, which is $a$.
$\Rightarrow$ Radius of the circle = $\frac{a}{2}$
$\Rightarrow$ Area of the circle = $\pi \times (radius{)}^2=\pi \times (\frac{a}{2}{)}^2=\frac{\pi a^2}{4}$

$\Rightarrow$Area of the shaded portion = $a^2-\frac{\pi a^2}{4}$
Hence, option c is correct.