Question

Which expression represents the area of the shaded region?

Answer 1

Given:

A circle of radius r inscribed in a square.

To find:

The expression for the area of the shaded region.

Solution:

Area of a circle is:

$A_1=\pi r^2$

Where, r is the radius of the circle.

Area of a square is:

$Area=a^2$

Where, a is the side of the square.

A circle of radius r inscribed in a square. So, diameter of the circle is equal to the side of the square.

$a=2a$

So, the area of the square is:

$A_2=(2r)^2$

$A_2=4r^2$

Now, the area of the shaded region is the difference between the area of the square and the area of the circle.

$A=A_2-A_1$

$A=4r^2-\pi r^2$

$A=4r^2-\pi r^2$

$A=r^2(4-\pi )$

Therefore, the correct option is (a).