Question

Someone please! Help Me ! Find the area of a regular hexagon given the side length is 4 in. Leave your answer in exact form (with square root) and no decimals. (Use sq rt as the square root symbol.

Answer 1

A regular hexagon is made up of 6 equilateral triangles, so

100 = 6(1/4 sqrt(3))* s^2

solve for s:

100 = 3/2 sqrt(3) s^2

s^2 = 100/(3/2 sqrt(3))

s^2 = 200/(3 sqrt(3))

s = sqrt(200/(3sqrt(3)) ~ = 6.2 cm

Answer 2

AB = 4
AC = AB/2 = 2
tan(60) = OC / AC
sqrt(3) = OC / 2
OC = 2 * sqrt(3)

Area of triangle = 1/2 * base * height = 1/2 * AB * OC = 1/2 * 4 * 2 * sqrt(3)
= 4 * sqrt(3)

Area of hexagon = 6 * area of triangle OAB = 6 * 4 * sqrt(3) = 24sqrt(3)

Answer 3

thank you so much :) !!!!

Answer 4

you are welcome.