# How to Measure Triangles

You can measure the perimeter and area of all triangles. There also is a special feature of right triangles that allows you to measure them more easily.

## Finding the perimeter and area of a triangle

Mathematicians have no special formula for finding the perimeter of a triangle — they just add up the lengths of the sides.

To find the area of a triangle, you need to know the length of one side — the *base* (*b* for short) — and the *height** **(h).* Note that the* *height forms a right angle with the base. This figure shows a triangle with a base of 5 cm and a height of 2 cm:

Here’s the formula for the area of a triangle:

So here’s how to figure out the area of a triangle with a base of 5 cm and a height of 2 cm:

## Finding the third side of a right triangle

The long side of a right triangle *(c)* is called the hypotenuse, and the two short sides (*a* and *b*) are called the *legs*:

The most important right triangle formula is the *Pythagorean theorem*:

This formula allows you to find the hypotenuse of a triangle, given only the lengths of the legs. For example, suppose the legs of a triangle are 3 and 4 units. Here’s how to use the Pythagorean theorem to find the length of the hypotenuse:

So when you multiply *c* by itself, the result is 25. Therefore, take the square root of both sides to find:

c= 5

The length of the hypotenuse is 5 units.