# How do you find the area of an equilateral triangle given the perimeter?

The area can be calculated as:

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To find the area of an equilateral triangle given the perimeter, divide the perimeter by 3 to find the length of one side (since all sides of an equilateral triangle are equal). Then, use the formula for the area of a triangle, which is (\frac{1}{2} \times \text{base} \times \text{height}). Since the triangle is equilateral, the height will bisect one of the sides, forming a right triangle with one of the sides and the bisected height. You can then use the Pythagorean theorem to find the height, which will be (\frac{\sqrt{3}}{2}) times the length of one side. Finally, substitute the side length and height into the area formula to find the area of the equilateral triangle.

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