 a (base)
in
b (base)
in
h (height)
in
Area
in²
Perimeter
c
in
d
in
Perimeter
in
Angles
α
deg
β
deg
γ
deg
δ
deg

# Area of a Trapezoid Calculator

By Bogna Haponiuk

If you ever had problems with remembering the formulas in geometry class, this area of a trapezoid calculator is bound to help you. In just a few simple steps, you will be able to find the area of a trapezoid and determine all of its other properties, such as side lengths or internal angles. So, if you are troubled by questions like "how to find the perimeter of a trapezoid", look no further - simply keep reading to find out!

You can also check out our circumference calculator to analyze the geometry of a circle in more detail.

## What is a trapezoid? A trapezoid is a 4-sided geometrical shape with two sides parallel to each other. These two sides (a and b in the image above) are called the bases of the trapezoid. The other two sides (c and d) are called legs. h is the height of the trapezoid.

All internal angles of a trapezoid sum to give 360°. Additionally, the angles on the same side of a leg are called adjacent and always sum up to 180°:

`α + β = 180°`

`γ + δ = 180°`

## How to find the area of a trapezoid?

Area of a trapezoid is found according to the following formula:

`A = (a + b) * h / 2`

You can notice that for a trapezoid with a = b (and hence c = d = h), the formula gets simplified to `A = a * h`, which is exactly the formula for the area of a rectangle.

## How to find the perimeter of a trapezoid?

You can also use the area of a trapezoid calculator to find the perimeter of this geometrical shape. Simply add all of the side lengths together:

`P = a + b + c + d`

## Using the area of trapezoid calculator: an example

Let's assume that you want to calculate the area of a certain trapezoid. All the data given is:

`α = 30°`

`γ = 125°`

`h = 6 cm`

`a = 4 cm`

`P = 25 cm`

1. Calculate the remaining internal angles. As `α + β = 180°`, `β = 180° - 30 ° = 150°`.

2. Similarly, as `γ + δ = 180°`, `δ = 180° - 125° = 55°`.

3. Find the lengths of the legs of the trapezoid, using the formula for the sine of an angle:

`sin 30° = c / h`

`sin 55° = d / h`

`c = sin 30° * 6 = 12 cm`

`d = sin 55° * 6 = 7.325 cm`

1. Subtract the values of a, c, and d from the trapezoid perimeter to find the length of the second base:

`b = P - a - c - d = 25 - 4 - 12 - 7.325 = 1.675 cm`

1. Finally, apply the formula for the area of a trapezoid:

`A = (a + b) * h / 2 = (4 + 1.675) * 6 / 2 = 17.026 cm²`

Make sure to take a quick look at the hexagon calculator, too!

Bogna Haponiuk