# What is the area of an equilateral triangle of side length 20 cm?

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#### Explanation

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8
Nov 26, 2015

$100 \sqrt{3}$

#### Explanation:

Referring to this image,
http://areeweb.polito.it/didattica/polymath/htmlS/argoment/ParoleMate/Gen_08/Img/TriangoloEquilatero%20(11)png
we know that $A B = A C = B C = 20$.

This means that the height cuts $A B$ in two equals parts, $A H$ and $H B$, each $10$ units long.

This means that, for example, $A H C$ is a right triangle with $A C = 20$ and $A H = 10$, so

$C H = \sqrt{A {C}^{2} - A {H}^{2}} = \sqrt{{20}^{2} - {10}^{2}} = \sqrt{300} = 10 \sqrt{3}$

Since we know the base and the height, then the area is

$\frac{20 \cdot 10 \sqrt{3}}{2} = 100 \sqrt{3}$

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