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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, a
^{2}= (a/2)^{2}+ h^{2} - so, h
^{2}= a^{2}- (a/2)^{2}= a^{2}- a^{2}/4 = (3/4)a^{2} - 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) a
^{2}/4.