Question

Find the area of the circle

a) 98π in²
b) 196π in²
c) 20π in²
d) 39π in²​

Answer 1

Given:

Square inscribed in a circle.

Side of square = 14 in

To find:

The area of the circle

Solution:

All sides of square are equal.

Using Pythagoras theorem to find the diagonal:

$\text{Diagonal}^2 = 14^2+14^2$

$\text{Diagonal}^2 = 2\times14^2$

Taking square root on both sides, we get

Diagonal = $14\sqrt{2}$

Diameter of the circle = Diagonal of square

                                   = $14\sqrt{2}$ in

Radius of the circle = $14\sqrt{2} \div 2 = 7\sqrt{2}$

Area of the circle formula:

$A= \pi r^2$

Substitute r value, we get

$A= \pi \times (7 \sqrt{2})^2$

$A= \pi \times 98$

$A= 98\pi$

The area of the circle is 98π in²​.