Question

A square is inscribed in a circle of radius $7cm$. Find area of the square

• A. $98$ $c{m}^2$
• B. $147$$c{m}^2$
• C. $196$ $c{m}^2$
• D. $49$ $c{m}^2$

Answer 1

The correct option is A $98$ $c{m}^2$

Given,
Radius of the circle=$7$cm
Let the side of the square be $a$cm.
A square when inscribed in a circle then the diameter of the circle must be diagonal of the square.
Therefore,
Diagonal of square=$\sqrt{a^2+a^2}$
=$\sqrt{2}a$
Now,
Diameter of the circle=$2\times 7$
=$14cm$
$=>\sqrt{2}a=14$
$=>a=\frac{14}{\sqrt{2}}$
$=>a=7\sqrt{2}cm$
Therefore,
Area of square=$a^2$
=$(7\sqrt{2}cm{)}^2$
=$\left(7\sqrt{2}cm\right)\left(7\sqrt{2}cm\right)$
=$98c{m}^2$