How do I find the length of a side of a regular hexagon with an area equal to that of the area of an equilateral triangle w/ a perimeter of 36 inches?

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The area of an equilateral triangle is (s^2 * √3)/4 where s is the length of a side. If you connect opposite vertices of the hexagon you create 6 congruent equilateral triangles. The triangle with perimeter has a side length of 12 so its area is (12^2*√3)/4 = 36√3 The area of the hexagon would be the area of 6 equilateral triangles or 6(s^2*√3)/4 Set this equal to the area of the triangle to get 6(s^2*√3)/4 = 36√3 Do the math and get x = √24 = 2√6