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

Answer 1

The area can be calculated as: #A=(p^2*sqrt(3))/36#

If we have a perimeter #p#, then we can calculate the side of the triangle as #a=p/3#. Knowing the side we can write area #A# as:

#A=(a^2*sqrt(3))/4=((p/3)^2*sqrt(3))/4=(p^2/9*sqrt(3))/4=(p^2*sqrt(3))/36#

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Answer 2

Sophia Alfred

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.