# #### Area of a Trapezoid

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

1. Identify the bases of the trapezoid.
2. Identify the height of the trapezoid.
3. 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:

$\red b_1=13$

$\red b_2=6$

$\red h=8$

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

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

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.