Question

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

Answer 1

`100sqrt(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 `AB=AC=BC=20`.

This means that the height cuts `AB` in two equals parts, `AH` and `HB`, each `10` units long.

This means that, for example, `AHC` is a right triangle with `AC=20` and `AH=10`, so

`CH = sqrt(AC^2-AH^2) = sqrt(20^2-10^2)=sqrt(300)=10sqrt(3)`

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

`(20*10sqrt(3))/2 = 100sqrt(3)`