Express answer in exact form. show all work for full credit.
find the area of one segment formed by a square with sides of 6" inscribed in a circle.
(hint: use the ratio of 1: 1: to find the radius of the circle.)

Given:
side of the square = 6 inches

Area of the square = (6 inches)² = 36 in²

To find the Area of the circle, we need to solve the diagonal of the square because it is the diameter of the circle. We will use the Pythagorean theorem to solve for the diagonal/hypotenuse.

6² + 6² = 36 + 36 = 72 
√72 = √36 * 2 = 6√2  measure of the diagonal/hypotenuse/diameter

radius = 6√2 / 2 = 3√2

Area of a circle = (3√2 in)² * 3.14
A = 18 in² * 3.14
A = 56.52 in²

Area of the circle - Area of the square → 56.52 in² - 36 in² = 20.52 in²

20.52 in² ÷ 4 segments = 5.13 in²

The area of one segment formed by a square with sides of 6" inscribed in a circle is 5.13 in².