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 = πr2
Area of circle A1 = 3.14 × (3√2)2
A1 = 3.14 × 9 × 2
A1 = 56.52 square inches
Area of the square A2 = a2
A2 = (6)2
A2 = 36 square inches
So the area of one segment = (A1 - A2) / 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.