I need help with a trig question.

Question

This has me stumped it sounds easy but I just dont know where to start, The question goes"A regular Hexagon contains six equilateral triangle with a common point at the center. If the height of one of those triangles is 10cm, Explain why the perimeter of the Hexagon is 69.28cm."

Answer 1

For an equilateral triangle all the angles equal 60° and the sides are equal length.

The problem says the height is 10 cm. If you bisected each triangle you would get two 30°-60°-90° triangles, with the 10 cm height adjacent to the 30° angle (I wish I could draw a sketch on here)

If we use tangent, we can find the length opposite of the 30°

tan 30 = x/10

.5774 = x/10

5.774 = x

Since x = 1/2 the length of the side of the equilateral triangle, if we double x we will find the length of each side of the equilateral triangle

2x = 11.55

Now we know that each side of the equilateral triangles is 11.55. If we multiply this by 6, we find the perimeter of the regular hexagon

11.55 * 6 = 69.28

Hope that helps, feel free to ask any follow up questions