Right Trapezoid Area Calculator

Created by Gabriela Diaz
Reviewed by Luciano Mino
Last updated: Sep 30, 2022

Welcome to the right trapezoid area calculator, where you'll be able to compute the area of any right trapezoid in a blink of an eye! 😉
Here we'll also learn:

  • What is a right trapezoid; and
  • How to find the area of a right trapezoid yourself, even if at first you don't know its height.

Shall we get started?

What is a right trapezoid?

A right trapezoid is a particular case of a trapezoid, a four-sided geometry with at least one pair of opposite sides parallel to each other. These parallel sides, also known as bases, are identified in the image below as aa and bb.

Right trapezoid

In the specific case of a right trapezoid, one of the two remaining sides, cc from the figure, is perpendicular to the parallel sides aa and bb, creating 90° angles (right angles) between them.

How to find the area of a right trapezoid

To find the area of a right trapezoid, use the formula: A = ( a + b ) x h/2.

Where:

  • A – Area of the trapezoid;
  • a and b – Bottom and top bases; and
  • h – The height.

Meaning that if you know all of these dimensions, you'll be able to calculate the area of your right trapezoid directly.

But what if you don't know the height h? Would you still be able to calculate the area? This is when some good old trigonometry comes to the rescue!

Right trapezoid

Looking at the image, we can see a right triangle forming from the height h, the difference of the bases (a - b) and the side d.

From here, if you know:

  • The two sides (a - b) and d; or
  • One side and one angle of the right triangle, you're all set!

If you know two sides, the calculation of h revolves around the Pythagorean theorem as:

  • h = √(d² - (a - b)²)

On the other hand, if you have one side and one angle, you can get the value of h by using the arcsine function (the inverse of the sine) as:

  • h = arcsin(δ) * d

or...

  • h = arcsin(γ - π/2) * d

💡 You can learn more about the arcsine trigonometric function with our arcsin calculator. For other trigonometric functions, check our trigonometry calculator!

How to use the right trapezoid area calculator

To use the right trapezoid area calculator:

  1. Input the bases a and b. For example, let's assume a = 10 and b = 6.
  2. Enter the value of the height h. In our example, suppose h = 4.
  3. The calculator will display the result for the area on the last row. For our calculation, we get A = 32. And that's it! 😀

💡 Don't know the value of the height h? Click on the Advanced mode button to get the value of the area by entering the angles and the slant side.

More trapezoid calculators

Now that you've learned how to calculate the area of a right trapezoid, why not read about the area of an irregular trapezoid or ultimately expand your knowledge about trapezoids with our trapezoid calculator.

To learn about specific topics concerning trapezoids, we recommend other of our tools:

FAQ

Can a trapezoid have exactly one right angle?

No, a trapezoid can't have only one right angle. The minimum amount of right angles a trapezoid can have is two. This configuration is known as a right trapezoid. The following number of right angles is four; this is the case of a rectangle.

How do I find the height of a right trapezoid?

To find the height of a right trapezoid you might meet one of these cases:

  • If the bases a and b, and the slant side d are known, use the Pythagorean theorem: h = √(d² - (a - b)²).
  • When knowing the slant side d and the acute angle δ use: h = arcsin(δ) x d.
  • If knowing the slant side d and the obtuse angle γ utilize: h = arcsin(γ - π/2) x d.
Gabriela Diaz
A trapezoid with sides, angles and height marked
a (base)
in
b (base)
in
h (height)
in
Area (A)
in²
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