Question

A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.

Answer 1

A segment of a circle has a 120 arc and a chord of 8in. The area of the segment = (120/360) x 3.14 x 8^2 = 67 in^2

Answer 2

`A = 22.342\,in^(2)`

Explanation:

The radius of the circle is:

`2\cdot r \cdot \cos 30^(\textdegree) = 8\,in`

`r = (8\,in)/(2\cdot \cos 30^(\textdegree))`

`r \approx 4.619\,in`

Finally, the area of the segment is:

`A = \left((120^(\textdegree))/(360^(\textdegree)) \right)\cdot \pi \cdot (4.619\,in)^(2)`

`A = 22.342\,in^(2)`