The area of a hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.

Question

mathstudent55 · Answer

A regular hexagon is made up of 6 equilateral triangles.
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mathstudent55 · Answer

The area of this hexagon is equal to the area of a large triangle.
That means each of the 6 triangles that makes up the hexagon is 1/6 the area of the triangle.

mathstudent55 · Answer

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mathstudent55 · Answer

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mathstudent55 · Answer

You have two similar equilateral triangles, a large one and a small one. The area of the large one is 6 times the area of the small one. If the areas are in a 6/1 ratio, what is the ratio of the lengths of the sides?

mathstudent55 · Answer

The sides are in a sqrt(6/1) ratio.
That is a ratio of sqrt(6)/1
That means the side of the small triangle measures sqrt(6).
The side of the small triangle is congruent to the side of the hexagon, so the side of the hexagon measure sqrt(6).

anonymous · Answer

thank you so much!!!  @mathstudent55

mathstudent55 · Answer

wlcm