Question

The perimeter of an equilateral triangle is 60 m.the area is​

Answer 1

173.21m^2

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:

`width*height = area`

This is a fairly simple formula, and works out nicely since our normal right triangle formula for area of
`(length*width)/(2)` 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.

`width = 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.

`hypotenuse = 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

`Hypotenuse=√(width^2+height^2)`, which we can rewrite to get:

`Height = √(hypotenuse^2-width^2)`

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

`Height = √(20^2-10^2)`

=

`Height = √(400-100)`

=

`Height = √(300)`

=

Height = 17.321

Now we can solve for the area using the formula from above,
`width*height = area`

=

`10*17.321 = 173.21`

So our area equals 173.21!

Hope this helps! :3