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Area of an equilateral triangle with side a

Question: In an equilateral triangle with side a, find the area of the triangle.

Solution:
Because the triangle is an equilateral triangle and the length of its each side is a (given), and
the area (A) of a triangle is: A = (1/2) base × altitude = (1/2) b h, where b is base and h is altitude to the base.
In our case, b = a, and the altitude to the base is h, now we need to find the value of h.
Because the triangle is an equilateral triangle, so its altitude cuts its base in half. So, its half base is (a/2).
In right triangle, a2 = (a/2)2 + h2
so, h2 = a2 - (a/2)2 = a2 - a2/4 = (3/4)a2
so, h = (square root of 3)a/2
so, A = (1/2)b h = (1/2)a × (square root of 3)a/2 = (square root of 3) a2/4.