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

Question

anonymous · Answer

Since it's a regular hexagon, all six sides are equal. The perimeter is the sum of the measurement of all sides. So we need to find the measurement of a side and multiply it by six.

anonymous · Answer

Except it's being composed of 12 right triangles rather than 6 equilateral triangles. I just did the math, and I believe if the hypotenuse is 18 times the square root of 3, you would divide that by two to find the shorter leg. Then you would get 9 times the square root of 3. After multiplying that by 12, you come out with 108 times the square root of 3.
Turns out I did know how to do this, I just had to draw out the hexagon and give myself a visual. I appreciate your help! Let me know what you think of my answer.

anonymous · Answer

|dw:1377132070234:dw|   the side opp the 30 will be 1/2 of a side of the hexagon. Since the hypotenuse measures 18 times the square root of 3, the shorter side will be equal to 18. since a side of the hexagon is two of these, one side = 36. Six sides so answer is 108.