The equilateral triangle formula

Geometry Level 2

Let S S denote the side length of an equilateral triangle. Which of the following represents the area of this triangle?

S S − S 2 S \sqrt{S - \frac S2} S S 2 + S 2 4 S \sqrt{S^2+\frac{S^2}4} S ( S 2 − S 2 4 ) 2 S \left (S^2-\frac{S^2}4\right)^2 There is no formula S 2 S 2 − S 2 4 \frac S2 \sqrt{S^2- \frac{S^2}4}

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2 solutions

Ron Gallagher
Jul 23, 2020

This is a special case of Heron's formula, with all the sides equal: https://en.wikipedia.org/wiki/Heron%27s_formula

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The area of a triangle is Base x Height, so we need to find both.

Using the Pythagorean theorem, we find the height of the triangle is (S^2-S^2/4)^1/2

The base is obviously 2, so the answer is Sx(S^2-S^2/4)^1/2.

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(basexheight)/2

ma pm - 1 year ago

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