Question

A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.

Answer 1

The angle subtended by one segment is 360/6 = 60 degrees. The area of the triangle is 1/2 * 3 * 3 + sin 60 = 9/4 * sqrt 3 . The area of the sector of the circle is 1/6 (pi * 3^2) = 9/6 * pi


So area of segment is sector minus triangle
9(pi/6 - (sqrt 3)/4)= 9((3.14/6) - (1.732/4))