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.)


help me

Answer 1

a hexagon has how many sides?

Answer 2

or if i think of this more easierly :)

a hexagon is made up of equilateral triangles; with sides of 3-3-3, and a central angle of 60

Answer 3

3^2 sin(60)/2 = area of triangle peice

60 degrees = pi/3 radians soo

the area of the sector is: (pi/3) (3^2)/2

area of little halfmoon segment is:

(pi/3)(9/2) - (9/2)(sqrt(3)/2)

Answer 4

with any luck its

9pi 9sqrt(3)
--- - ------- simplify as needed
6 4

Answer 5

little halfmoon segment :) sounds like a character from a mathematical fairy tale book.

Answer 6

lol :)