Irregular Trapezoid Area Calculator

Created by Davide Borchia
Reviewed by Gabriela Diaz
Last updated: Mar 14, 2022

Quickly calculate the area of an irregular trapezoid with our calculator! Here you will learn:

  • How to find the area of a trapezoid;
  • How to use our irregular trapezoid area calculator.

What is a trapezoid?

A trapezoid is a four-sided (quadrilateral) two-dimensional shape with a pair of parallel sides, the bases and two not necessarily parallel sides, the legs.

🙋 If there are no parallel sides, the shape is called trapezium: we don't do that here!

The distance between the parallel sides is called height. In the image below you can see all the trapezoid elements:

trapezoid image
The elements of a trapezoid.

You can identify:

  • The two bases, aa and bb;
  • The two legs, cc and dd;
  • The height, hh; and
  • Four angles, α\alpha, β\beta, γ\gamma, and δ\delta.

The angles of a trapezoid must satisfy the following equalities:

  • α+β=180°\alpha+\beta=180\degree;
  • γ+delta=180°\gamma+delta=180\degree.

This means that the total sum must be 360°360\degree. Also, the angles associated with the same legs are complementary.

There are many types of trapezoids: here, we will focus on irregular trapezoids: the two legs have different lengths.

How to find the area of a trapezoid—irregular or not!

Calculating the area of an irregular trapezoid is not a big deal. In the end, you only need the value of the bases and the height!

The formula for the area of an irregular trapezoid is:

A=a+b2hA=\frac{a+b}{2}\cdot h

There is an easy—and beautiful proof of this. Remember the formula for the area of a triangle: A=bh2A=\frac{b\cdot h}{2}, and now take your irregular trapezoid, a pair of scissors, and cut!

If you cut on the line connecting one of the angles to the midpoint of the opposite leg, you can then join the two new shapes on the half-side, like in the diagram below:

Trapezoid area
How to find the area of an irregular trapezoid.

Now you have a triangle with height hh and base a+ba+b. You know how to find its area!

How to use out irregular trapezoid area calculator

To find the area of an irregular trapezoid, simply insert the values of the bases and the height in our calculator!

You can also use our calculator in reverse, inserting the area and finding either the bases or the height.

🙋 We hid some functionalities in the advanced mode. There are ways to find the values of bases and height when you know the angles or the legs: if you need it, we got your back: insert the parameter you have, and find the area!

For example, assume you have a really "short" trapezoid, with bases a=10 cma=10\ \text{cm}, b=6 cmb=6\ \text{cm}, and height h=2 cmh=2\ \text{cm}. Input the values in our calculator!

We will compute this expression for you:

A=a+b2h=10+622 cm2=16 cm2\footnotesize A=\frac{a+b}{2}\cdot h=\frac{10+6}{2}\cdot 2\ \text{cm}^2= 16\ \text{cm}^2

Discover our other trapezoid calculators!

We have many other calculators that can help you with your trapezoidal problems! 😉

Try our general trapezoid calculator, or for more specific questions, explore our plethora of tiny calculators:

FAQ

What is the formula of the area of an irregular trapezoid?

The formula for the area of an irregular trapezoid is:
A = (a+b) * h/2
Where

  • a and b are the bases of the trapezoid; and
  • h is the height of the trapezoid.

Does the area of a trapezoid depend on the legs?

The oblique sides of a trapezoid, or legs, don't appear in the area formula! Only the height of the trapezoid and the bases affect the value of the area!

This means that it doesn't matter if you consider a scalene trapezoid (all the sides different in value), a right trapezoid, or an isosceles one: as long as bases and height don't change, the area remains the same.

What is the area of an irregular trapezoid with bases a=8, b=2, height h=4, and a side c=5?

Apply the formula for the area of the trapezoid:
A = (a + b) * h/2 = (8 + 2) * 4/2 = 20

The area of this trapezoid is 20. The value of the last side didn't enter the calculations! Find out how to calculate the area of an irregular trapezoid on omnicalculator.com.

How do you find the area of a trapezoid using two triangles?

To find the area of a trapezoid geometrically, cut the trapezoid on a line connecting a vertex to the midpoint of the opposite side.

Rotate the shape you find until you make the two half sides fit together. At this point, you should have a segment of length equal to the sum of the two bases, which is the base of a triangle with height equal to the one of the trapezoid. From here, apply the area of a triangle formula:
A = b * h/2
where b is the base, and h is the height.

You are all set!

Davide Borchia
A trapezoid with sides, angles and height marked
a (base)
in
b (base)
in
h (height)
in
Area
Area (A)
in²
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