Find your Math Personality!

Find your Math Personality!

# Find the area of one segment formed by a square with sides of 6" inscribed in a circle.

**Solution:**

The diagonal D of the square with side a is

D = a√2

If a = 6 inches

d = D = 6√2 inches

Radius r = 6√2/2 = 3√2 inches

We know that the area of the circle = πr^{2}

Area of circle A_{1} = 3.14 × (3√2)^{2}

A_{1} = 3.14 × 9 × 2

A_{1} = 56.52 square inches

Area of the square A_{2} = a^{2}

A_{2} = (6)^{2}

A_{2} = 36 square inches

So the area of one segment = (A_{1} - A_{2}) / 4

= (56.52 - 36) / 4

= 20.52 / 4

= 5.13 square inches

Therefore, the area of one segment is 5.13 square inches.

## Find the area of one segment formed by a square with sides of 6" inscribed in a circle.

**Summary:**

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

Math worksheets and

visual curriculum

visual curriculum