Question

What is the height and area of an equilateral triangle with a base of 10 meters?

Answer 1

`h=5sqrt3" m"`
`A=25sqrt3" m"^2`

Explanation:

We can see that if we split an equilateral triangle in half, we are left with two congruent equilateral triangles. Thus, one of the legs of the triangle is `1/2s`, and the hypotenuse is `s`. We can use the Pythagorean Theorem or the properties of `30˚-60˚-90˚` triangles to determine that the height of the triangle is `sqrt3/2s`.

If we want to determine the area of the entire triangle, we know that `A=1/2bh`. We also know that the base is `s` and the height is `sqrt3/2s`, so we can plug those in to the area equation to see the following for an equilateral triangle:

`A=1/2bh=>1/2(s)(sqrt3/2s)=(s^2sqrt3)/4`

Since `s=10`, `A=(10^2sqrt3)/4=(100sqrt3)/4=25sqrt3" m"^2`

Also, since the height is `sqrt3/2s`, we can say the height is `5sqrt3" m"`.