Mathematics
: asked on shoreelinee1337

31.03.2022

0

09.07.2023, solved by verified expert

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173.21m^2

Step-by-step explanation:

So lets figure out how to find the formula for the area of a equilateral triangle.

We can immediatly notice that a equilaterial triangle is really just two right triangles merged together at their heights.

This means that the total area of the equilaterial triangle is equivelent to finding the area of 2 right triangles. this would make the formula:

This is a fairly simple formula, and works out nicely since our normal right triangle formula for area of must be multiplied by 2 since there are two right triangles.

The problem is, how we will actually find h, the height.

Each side length of a equilateral triangle equals 1/3 of the perimeter, meaning that each side length is 20.

W, the width of each right triangle is 1/2 of the side length of the equilateral triangle, meaning that the width equals 10.

We also know that the hypotenuse of the triangle is equal to the side length of the equilateral triangle, which means that the hypotenuse equals 20.

We can use this to figure out our unknown height, which we can then use to find our area.

We can figure out this height using teh pythagreon theorm, since

, which we can rewrite to get:

Now we can plug in our hypotenuse and width to solve:

=

=

=

Height = 17.321

Now we can solve for the area using the formula from above,

=

So our area equals 173.21!

Hope this helps! :3

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