How do you calculate the height of an equilateral triangle?

Nov 26, 2015

The height of the equilateral triangle is $h = \frac{a \sqrt{3}}{2}$

Explanation:

If you draw a height in an equilateral triangle you can see that the triangle is divided in 2 right angled triangles in which: sides $a$ are hypothenuses, height is one cathetus (common for both triangles), the other is equal to $\frac{a}{2}$, so if we use the Pythagorean theorem we get:

${\left(\frac{a}{2}\right)}^{2} + {h}^{2} = {a}^{2}$

${h}^{2} = {a}^{2} - {\left(\frac{a}{2}\right)}^{2}$

${h}^{2} = {a}^{2} - {a}^{2} / 4$

${h}^{2} = \frac{3}{4} {a}^{2}$

$h = \frac{a \sqrt{3}}{2}$