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Question

An isoceles trapezoid may be divided into 3 congruent non-overlapping equilateral triangles. The area of each triangle is 9 square root 3 , square inches. What is the number of inches in the perimeter of the trapezoid?

Answer 1

The area of any triangle is 1/2 b*h.
For an equilateral triangle, b is the edge length, and h is sqrt(3)/2 times the edge length.

So, let's use that formula and call "e" the edge length of the equilateral triangle:

a = 1/2 b * h
9 sqrt(3) = 1/2 e * e * sqrt(3)/2
9 = (e^2)/4
36 = e^2
e = 6

This trapezoid has five equilateral triangle edges to its perimeter: one on the shorter base, two on the longer base, and one on each sloped side, so:

p = 5 * e
p = 5 * 6
p = 30 inches

Answer 2

Your isosceles trapezoid is half of a regular hexagon.

The area of each equilateral triangle is 1/2 b h.

b = s, the side
and h = sqrt(3)/2 s

At = 1/2 s sqrt(3)/2 s
At = sqrt(3)/4 s^2

9sqrt(3) sqin = sqrt(3)/4 s^2
36 sqin =s^2
6 in =s

counting the sides of the triangles going around the trapezoid, we find there are 5 of them.

5s = 30 in

Answer 30 in

Answer 3

the area of an equilateral is:
A = sqrt(3)/4 * s^2

9sqrt(3) = sqrt(3)/4 * s^2

36sqrt(3) = sqrt(3) * s^2

36 = s^2

s = 6in

so, the sides of the equilateral is 6ins

Draw a diagram and you'll see the perimeter is:
6 + 6 + 6 + 6 + 6 = 30in