What is area of equilateral triangle?

1 Answer
George C.
Jun 15, 2015

If the sides of an equilateral triangle are all of length #a#, then the area is #sqrt(3)/4a^2#

Explanation:

Consider an equilateral triangle with sides of length #a#.

If you bisect it to make two right angled triangles, then those triangles will have hypotenuse of length #a#, shortest side of length #a/2# and other side of length:

#sqrt(a^2-(a/2)^2) = sqrt(a^2-a^2/4) = sqrt((3a^2)/4) = (sqrt(3)a)/2#

The two right angled triangles can be rearranged (turning one over) into a rectangle with sides #(sqrt(3)a)/2# and #a/2#.

The area of the rectangle, which is the same as the area of the original triangle is:

#(sqrt(3)a)/2*a/2 = sqrt(3)/4a^2#

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