Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 9-inch perimeter A = sq. in.

Step-by-step explanation:

The area of a triangle is given by

where

b is the base

h is the height

Here we have an equilateral triangle, which has the 3 sides of the same length.

Let's call L the length of one side.

We know that the perimeter of the triangle is

p = 9 in

The perimeter is the sum of the three sides, so:

Therefore, we find the length of the side:

Therefore the length is the base of the triangle,

The height can be calculated by considering half triangle: the hypothenuse is equal to L, while one side is equal to half the base (b/2), therefore the height is given by Pythagorean's theorem:

Therefore, the area of the triangle is:

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step-by-step explanation: