Question

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

Answer 1

108 sqrt 3? right?

Answer 2

Yep.

Answer 3

thank you @coreylvaughn

Answer 4

how

Answer 5

Two cases:
1) A hypotenuse makes up one of the hexagon's sides. That's easy math.
2) We create an apothem. The hypotenuse (2x) is given as 18 root 3. Thus the x is 9 root 3. Two of those x's make up a side of the hypotenuse. Giving the same result as if we had just gone with case 1 above.

Answer 6

I made the assumption for x's value in case 2 based on the fact that the triangles are all 30-60-90.

Answer 7

No problem. Thanks @ramya25! :) Take care to you both!

Answer 8

gotcha thanks :)