Home > Pre-Algebra > Area > Area of a Trapezoid

## Area of a Trapezoid

#### Introduction

A trapezoid is a four-sided polygon with only one pair of parallel sides. A parallelogram is a type of trapezoid that has two pairs of parallel sides.

#### Terms

Area - A quantity that expresses the extent of a two-dimensional shape.
Parallelogram - A four-sided polygon with opposite sides parallel.
Polygon - A plane figure with at least three sides.
Trapezoid - A quadrilateral with only one pair of parallel sides.

## Lesson

Area of a Trapezoid Formula $ext{Area} = rac{a+b}{2} * h$

where a is the top base, b is the bottom base, and h is the height of the trapezoid. Note that $rac{a+b}{2}$ is the average length of the top and the bottom and that if a=b, the area becomes a*h, which is the area of a parallelogram.

If a trapezoid has a base of length 4, top of length 6, and height of 2, for example, the area is

$ext{Area} = rac{a+b}{2} imes h$

$ext{Area} = rac{4+6}{2} imes 2$

$ext{Area} = 5 imes 2$

$ext{Area} = 10$

## Examples

#### Area of a Trapezoid

$\text{Area} = \dfrac{1}{2} * (\text{Base1 + Base2}) * \text{Height}$
$\text{Area} = \dfrac{1}{2} * (10 + 14) * 10$
$\text{Area} = \dfrac{1}{2} * 24 * 10$
$\text{Area} = 120$
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