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

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Answer 1 · 2015-11-26T12:31:59

$100sqrt(3)$

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

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