Question

Express answer in exact form.

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.

(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3.)

Answer 1

A = { 3/2 π - 9/4 √ 3 } in^2

Explanation:

Hope it helps, sorry for answering late.

Answer 2

A - area of a segment formed by a side of the hexagon and the circle
A = {area of a sector of a circle} - {area of an equilateral triangle}


`A= (r^2\pi\alpha)/(360^o) - (r^2√(3))/(4)= (3^2\pi 60^o)/(360^o) - (3^2√(3))/(4)=(9\pi )/(6) - (9√(3))/(4)= (9)/(2) ((\pi )/(3) - (√(3))/(2))`