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Answer:
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:
[tex]width*height = area[/tex]
This is a fairly simple formula, and works out nicely since our normal right triangle formula for area of [tex]\frac{length*width}{2}[/tex] 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.
[tex]width = 10[/tex]
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.
[tex]hypotenuse = 20[/tex]
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
[tex]Hypotenuse=\sqrt{width^2+height^2}[/tex], which we can rewrite to get:
[tex]Height = \sqrt{hypotenuse^2-width^2}[/tex]
Now we can plug in our hypotenuse and width to solve:
[tex]Height = \sqrt{20^2-10^2}[/tex]
=
[tex]Height = \sqrt{400-100}[/tex]
=
[tex]Height = \sqrt{300}[/tex]
=
Height = 17.321
Now we can solve for the area using the formula from above, [tex]width*height = area[/tex]
=
[tex]10*17.321 = 173.21[/tex]
So our area equals 173.21!
Hope this helps! :3
