Question

5. In the figure, a square is inscribed in a circle. The side of the square is 10 cm. Find the area of the shaded region. (i = 3.14)
(1) 57 cm (2) 157 cm (3) 75 cm? (4) 100 cm​

Answer 1

The area of Shaded Region (The region outside square and inside circle) is

$57 cm^2$

As we know that side of square is 10 cm,

Using Pythagoras Theorem its diagonal is $10\sqrt{2}$.

As the diagonal of the square is a straight line which passes through the center of the circle and touches it at 2 points, it is also the diameter of the circle.

Using this, radius of the circle comes out to be $5\sqrt{2}$.

Using area of circles,

=3.14 x $r^{2}$

= 157 $cm^2$

Now, area of Square is = 10 x 10 = 100 $cm^2$

Subtracting the area, we get 57$cm^2$, which is the area of the shaded region