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:
\[\red b_1=13\]
\[\red b_2=6\]
\[\red h=8\]
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.
