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Sindrei [870]
3 years ago
9

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

Mathematics
1 answer:
Alona [7]3 years ago
5 0

Answer:

3.9 in^2

Step-by-step explanation:

The area of a triangle is given by

A=\frac{1}{2}bh

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:

p=L+L+L=3L

Therefore, we find the length of the side:

L=\frac{p}{3}=\frac{9}{3}=3 in

Therefore the length is the base of the triangle,

b=L

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:

h=\sqrt{L^2-(\frac{b}{2})^2}=\sqrt{3^2-(\frac{3}{2})^2}=2.6 in

Therefore, the area of the triangle is:

A=\frac{1}{2}(3)(2.6)=3.9 in^2

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