Question

If a circle is inscribed in a square as shown in the below figure. If the centre of the circle is (8,2) and (1,2) is a point on the square and circle then the area of the shaded region is ___ (take π = $\frac{22}{7}$)

• A. 100cm²
• B. 54cm²
• C. 86cm²
• D. 78.4cm²

Answer 1

The correct option is D

78.4cm²

Given the centre of the circle is (8,2) and a point on the circle is (1,2).

$\therefore$ Radius of the circle = $\sqrt{(8-1{)}^2+(2-2{)}^2}$

($\because$ Distance between points $(x_1,y_1)$ and$(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$)

= $\sqrt{7^2}$

= 7

$\therefore$ Area of the circle = $\pi \times radiu{s}^2$

= $\frac{22}{7}\times 7\times 7$

= 154 sq.units

Now the side of a square = diameter of the circle

= 2 $\times$ radius

= 14 units

$\therefore$ Area of the square = 14 $\times$ 14

= 196 sq.units

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

= 196 - 154

= 42 sq.units