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

Mar 18, 2016

$\text{area} = \frac{4 \sqrt{3}}{3}$

$\text{perimeter} = 4 \sqrt{3}$

#### Explanation:

If you bisect an equilateral triangle with sides of length $2 x$, then you get two right angled triangles with sides of length $2 x$, $x$ and $\sqrt{3} x$, where $\sqrt{3} x$ is the height of the triangle.

In our case, $\sqrt{3} x = 2$, so $x = \frac{2}{\sqrt{3}} = \frac{2 \sqrt{3}}{3}$

The area of the triangle is:

$\frac{1}{2} \times b a s e \times h e i g h t = \frac{1}{2} \times 2 x \times 2 = 2 x = \frac{4 \sqrt{3}}{3}$

The perimeter of the triangle is:

$3 \times 2 x = 6 x = \frac{12 \sqrt{3}}{3} = 4 \sqrt{3}$