What is the area of an equilateral triangle if you're given the length of one side?

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Answer 1 · 2015-11-29T21:01:54

The figure below shows an equilateral triangle with side $a$ and height $h$

enter image source here

The area of any triangle is given by the formula

$E=1/2*height*base$

in our case the height is $h^2=a^2-a^2/4=3*a^2/4=>h=sqrt3/2*a$

(We apply the Pythagorean theorem to find the height)

because it is an equilateral triangle with side $a$

so we have that

$E=1/2*sqrt3/2*a*a=sqrt3/4*a^2$