Question

Please help!
Express answer in exact form.

An equilateral triangle is inscribed in a circle with a radius of 6". Find the area of the segment cut off by one side of the triangle.

Answer must be in the form A= [XX*pi -x(sqrt x)] inches squared

Answer 1

since central angle is 120 degrees and 120/360 = 1/3
area of sector of circle is (1/3)*36pi = 12pi

for area of triangle, you can split it into 2 30-60-90 right triangles
with sides 3:3sqrt3:6
thus base of triangle is 6sqrt3 and height is 3
Area = 1/2 * 3* 6sqrt3 = 9sqrt3

--> segment area = 12pi - 9sqrt3