Express answer in exact form. Show all work for full credit.
2 answers:
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
<span>The area of one segment formed by a square with sides of 6" inscribed in a circle is 5.13 in</span>².
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
<span>The area of one segment formed by a square with sides of 6" inscribed in a circle is 5.13 in</span>².
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