Question

What is the area and perimeter of an equilateral triangle with height 2?

Answer 1

`"area" = (4sqrt(3))/3`

`"perimeter" = 4sqrt(3)`

Explanation:

If you bisect an equilateral triangle with sides of length `2x`, then you get two right angled triangles with sides of length `2x`, `x` and `sqrt(3)x`, where `sqrt(3)x` is the height of the triangle.

In our case, `sqrt(3)x = 2`, so `x = 2/sqrt(3) = (2sqrt(3))/3`

The area of the triangle is:

`1/2 xx base xx height = 1/2 xx 2x xx 2 = 2x = (4sqrt(3))/3`

The perimeter of the triangle is:

`3 xx 2x = 6x = (12 sqrt(3))/3 = 4sqrt(3)`