The area of a trapezoid is very easy to calculate once you know the formula.

\[A=\frac{1}{2}h(b_1+b_2)\]

On this page, I will use the formula to calculate the area of a trapezoid for some simple examples. To see more advanced examples, please check out my Area of a Trapezoid Formula page.

## How to Find the Area of a Trapezoid

- Identify the bases of the trapezoid.
- Identify the height of the trapezoid.
- Plug those numbers into the Area of a Trapezoid Formula and simplify.

## Examples

Find the area of the trapezoid.

*What are the bases of the trapezoid?*

The \(8 \, cm\) and \(15 \, cm\) sides are parallel to each other, so…

\[\blue b_1=8\]

\[\blue b_2=15\]

*What is the height of the trapezoid?*

The \(5 \, cm\) measurement is perpendicular to the bases so…

\[\blue h=5\]

The \(6 \, cm\) and \(6.2 \, cm\) measurements are slant heights and they are not necessary to find the area of the trapezoid.

*What is the area of the trapezoid?*

In Steps 1 and 2, I defined these variables:

\[\blue b_1=8\]

\[\blue b_2=15\]

\[\blue h=5\]

To find the area of the trapezoid, I will substitute these values into the Area of a Trapezoid Formula.

\[A=\frac{1}{2}({\blue 5})({\blue 8}+{\blue 15})\]

I can simplify the equation by adding \(\blue 8\) and \(\blue 15\).

\[A=\frac{1}{2}({\blue 5})(23)\]

Then I can simplify it further by multiplying \(\frac{1}{2}\), \(\blue 5\), and \(23\).

\[A=57.5\]

The area of the trapezoid is \(\blue 5.75 \, cm^2\).

Find the area of the trapezoid.

*What are the bases of the trapezoid?*

The \(4 \, in\) and \7 \, in\) sides are parallel to each other, so…

\[\yellow b_1=4\]

\[\yellow b_2=7\]

*What is the height of the trapezoid?*

The \(3 \, in\) measurement is perpendicular to the bases so…

\[\yellow h=3\]

The \(3.6 \, in\) and \(3.1 \, in\) measurements are slant heights and they are not necessary to find the area of the trapezoid.

*What is the area of the trapezoid?*

In Steps 1 and 2, I defined these variables:

\[\yellow b_1=4\]

\[\yellow b_2=7\]

\[\yellow h=3\]

To find the area of the trapezoid, I will substitute these values into the Area of a Trapezoid Formula.

\[A=\frac{1}{2}({\yellow 3})({\yellow 4}+{\yellow 7})\]

I can simplify the equation by adding \(\yellow 4\) and \(\yellow 7\).

\[A=\frac{1}{2}({\yellow 3})(11)\]

Then I can simplify it further by multiplying \(\frac{1}{2}\), \(\blue 3\), and \(11\).

\[A=16.5\]

The area of the trapezoid is \(\yellow 16.5 \, in^2\).

Find the area of the trapezoid.

*What are the bases of the trapezoid?*

The \(3 \, ft\) and \(10 \, ft\) sides are parallel to each other, so…

\[\green b_1=3\]

\[\green b_2=10\]

*What is the height of the trapezoid?*

The \(4 \, ft\) measurement is perpendicular to the bases so…

\[\green h=4\]

The \(5 \, ft\) and \(5.7 \, ft\) measurements are slant heights and they are not necessary to find the area of the trapezoid.

*What is the area of the trapezoid?*

In Steps 1 and 2, I defined these variables:

\[\green b_1=3\]

\[\green b_2=10\]

\[\green h=4\]

To find the area of the trapezoid, I will substitute these values into the Area of a Trapezoid Formula.

\[A=\frac{1}{2}({\green 4})({\green 3}+{\green 10})\]

I can simplify the equation by adding \(\green 3\) and \(\green 10\).

\[A=\frac{1}{2}({\green 4})(13)\]

Then I can simplify it further by multiplying \(\frac{1}{2}\), \(\green 4\), and \(13\).

\[A=26\]

The area of the trapezoid is \(\green 26 \, ft^2\).

Find the area of the trapezoid.

*What are the bases of the trapezoid?*

The \(13 \, mm\) and \(6 \, mm\) sides are parallel to each other, so…

\[\red b_1=13\]

\[\red b_2=6\]

*What is the height of the trapezoid?*

The \(8 \, mm\) measurement is perpendicular to the bases so…

\[\red h=8\]

The unknown side length and the \(12 \, mm\) measurement are slant heights and they are not necessary to find the area of the trapezoid.

*What is the area of the trapezoid?*

In Steps 1 and 2, I defined these variables:

\[\red b_1=13\]

\[\red b_2=6\]

\[\red h=8\]

\[A=\frac{1}{2}({\red 8})({\red 13}+{\red 6})\]

I can simplify the equation by adding \(\red 13\) and \(\red 6\).

\[A=\frac{1}{2}({\red 8})(19)\]

Then I can simplify it further by multiplying \(\frac{1}{2}\), \(\red 8\), and \(19\).

\[A=76\]

The area of the trapezoid is \(\red 76 \, mm^2\).

## Why It Works

Click here to see where the Area of a Trapezoid Formula comes from.