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.)

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.)

anonymous · Answer

In the hint part, it's s^2. sorry about that.

jim_thompson5910 · Answer

Area of one equilateral triangle:

A = (1/4)*s^2*sqrt(3)

A = (1/4)*3^2*sqrt(3)

A = (1/4)*9*sqrt(3)

A = (9/4)*sqrt(3)

--------------------------------------------

The radius is equal to the side length of the equilateral triangle (drawing a pic really helps see this), so r = 3


So the area of the circle is 

A = pi*r^2

A = pi*(3)^2

A = 9pi


So the area one-sixth of the circle is A = 9pi/6 = 3pi/2


Therefore, the answer is


3pi/2 -  (9/4)*sqrt(3)