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?

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

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