Answer:
Perimeter = 60√3
Step-by-step explanation:
I can't see any other way of doing this than by using trig.
Draw IS which is also 30.
- At the mid point of IS, the length of I to the midpoint is 15.
- Next from O, draw OL, OI, OW. You have drawn 3 lines and created 4 triangles.
- Each triangle has 180 degrees.
- The size of the interior angle is 180 * 4/6 which is 120
- The two remaining angles are each equal (the hexagon is regular) They both = (180 - 120) / 2 = 30
- The size of <SIL = 30 degrees.
Now we use that midpoint. Cos(30) = 15/IL
Cos(30) = √3/2 = adjacent / hypotenuse
The adjacent side = 15
15/(√3/2) = hypotenuse
Hypotenuse = 15*2 √3 / 3 = 10 √3
The hypotenuse is IL which is one of the sides.
The perimeter = 6*IL = 6 * 10 √3 = 60√3
Your answer is very close to mine. I'd sure like to know how you did it.
