Question

. A regular hexagon is composed of 12 congruent 30 o -60 o -90 o triangles. If the length of the hypotenuse of one of those triangles is 18 square root 3 , find the perimeter of the hexagon.

Answer 1

see the attached figure to better understand the problem

Let

2L---------> lenght side of hexagon

we know that

in one of those triangles

sin 30=1/2

sin 30=L/hypotenuse

solve for L

L=hypotenuse*sin 30-------->L=( 1 8 √ 3 )*(1 /2)------> L=9√3 units

Find the perimeter

perimeter=(2L)*6--------> L*12-------> Perimeter=9√3*12--------->108√3 units

therefore

the answer is

the perimeter of the regular hexagon is 108√3 units