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

The area to be determined is a segment of the circle.

Since central angle is 120 degrees and 120/360 = 1/3

area of sector of circle is (1/3)*36pi = 12pi

For the 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

I just did this so I know it's correct.

the first option is the answer.

-9

step-by-step explanation: