Question

A circle is inserted inside a square, such that the edge of the circle touches the sides of the square.If the side of the square is 14 cm, then the area of the shaded portion will be __ sq.cm.

• A. 42
• B. $44c{m}^2$
• C. $46c{m}^2$
• D. $50c{m}^2$

Answer 1

The correct option is A 42

Here we are asked to find the area of the shaded area.
The area of the shaded area should be the difference between the area of the square and the area of the circle.

Here we are given the side of the square,
x = 14 cm
Therefore, Area of the square
$=x^2={14}^2$
$=196c{m}^2$

The radius of the circle will be, $r=\frac{d}{2}$

$r=\frac{14}{2}=7cm$

Area of the circle,

$A=\pi \times r^2(use\pi =\frac{22}{7})=\left(\frac{22}{7}\right)\times 7^2=154c{m}^2$

Area of the shaded portion = Area of the square - Area of the circle

$=196-154=42c{m}^2$

Therefore, the area of the shaded portion will be
$42c{m}^2$