# How Do You Find the Perimeter and Area of a Trapezoid?

So far we have learned about the perimeter and area of a square, a rectangle, a rhombus and a parallelogram. Now we will look at how to find the perimeter and area of a trapezoid. But first, let’s take a look at one.

A trapezoid is a quadrilateral with two parallel sides of differing lengths. The other two sides can be at any length—and any angle!

## Perimeter of a Trapezoid

To find the perimeter you need to add the length of all four sides. In a trapezoid, the four sides can, and usually are, all different lengths, so all four sides must be measured out and added together.

Formula

### PerimeterofaTrapezoid

Two sides are parallel, but not the same length.

 $P={\text{side}}_{1}+{\text{side}}_{2}+{\text{side}}_{3}+{\text{side}}_{4}$

Example 1

Find the perimeter of the following trapezoid:

You use the formula and add all four sides together: $\begin{array}{llll}\hfill P& =2\phantom{\rule{0.17em}{0ex}}\text{cm}+3\phantom{\rule{0.17em}{0ex}}\text{cm}+3\phantom{\rule{0.17em}{0ex}}\text{cm}+5\phantom{\rule{0.17em}{0ex}}\text{cm}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =13\phantom{\rule{0.17em}{0ex}}\text{cm}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

## Area of a Trapezoid

To find the area of a trapezoid you need to know the length of the two parallel sides and the height of the trapezoid. When you know this, you put the numbers into the following formula for the area of a trapezoid.

Formula

### AreaofaTrapezoid

 $A=\frac{\left(a+b\right)\cdot h}{2}$

The height is always a right angle to both the parallel sides. When you know the two lengths and the height, you can use the formula.

Example 2

Find the area of the trapezoid

You find the area by using the formula: $\begin{array}{llll}\hfill A& =\frac{\left(4\phantom{\rule{0.17em}{0ex}}\text{cm}+2\phantom{\rule{0.17em}{0ex}}\text{cm}\right)\cdot 3\phantom{\rule{0.17em}{0ex}}\text{cm}}{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{6\phantom{\rule{0.17em}{0ex}}\text{cm}\cdot 3\phantom{\rule{0.17em}{0ex}}\text{cm}}{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{18\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{2}}{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =9\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$