# Trapezoids: Area and Perimeter

A
**
trapezoid
**
, also called a
**
trapezium
**
in some countries, is a
quadrilateral
with exactly one pair of
parallel
sides.

The parallel sides are called the
**
bases
**
and the non-parallel sides are the
**
legs
**
of the trapezoid.

An
**
isosceles trapezoid
**
is a trapezoid in which the two non-parallel sides are
congruent
.

The area $A$ of a trapezoid is given by

$A=\frac{{b}_{1}+{b}_{2}}{2}h$

where ${b}_{1}$ and ${b}_{2}$ are the lengths of the two parallel sides, and $h$ is the height, as shown in the figure below.

The perimeter of a trapezoid is the sum of the lengths of its four sides. If one or more of the lengths is not known, you can sometimes use the Pythagorean Theorem to find it.

**
Example:
**

Find the area and perimeter of the trapezoid shown.

To find the area, apply the formula.

$\begin{array}{l}A=\frac{{b}_{1}+{b}_{2}}{2}h\\ =\frac{3+11}{2}\left(7\right)\\ =7\left(7\right)\\ =49\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{square}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{units}\end{array}$

To find the perimeter, add the lengths of all four sides.

$\begin{array}{l}P=3+10+11+8\\ =32\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{units}\end{array}$