Question

a square of area 64 CM square is inscribed in a circle find the area of the circle​

Answer 1

SOLUTION:-

Given:

A square area is 64cm².

So,

We know that area of square= side×side.

Or

s²

=) s² = 64

=) s= √64

=) s= 8cm.

The diagonal is the diameter of the circle, hence join the diagonal.

Therefore,

Make a triangle, we get;

Using Pythagoras Theorem:

=) (diagonal)² = 8² + 8²

=) (diagonal)² = 64 + 64

=) (diagonal)² = 128

=) diagonal = 8√2cm

&

The diagonal is the diameter of the circle, so the radius of the circle is d/2.

=) 8√2/2

=) 4√2cm

Now,

We know area of circle= πr².

$= > \frac{22}{7} \times (4 \sqrt{2} ) \times (4 \sqrt{2} ) \\ \\ = > \frac{22}{7} \times 4 \times 1.414 \times 4 \times 1.414 \\ \\ = > \frac{70 3.78}{7} {cm}^{2} \\ \\ = > 100.54 {cm}^{2}$

Hence,

The area of circle is 100.54cm².

Hope it helps ☺️