Trapezoid Area Calculator

Math Geometry • Basic Shapes and Properties

Written by STEM Calculators Team Published January 21, 2026 Updated February 24, 2026

Calculate trapezoid area from the two parallel bases and height: \(A=\dfrac{a+b}{2}\,h\).

Inputs accept 1e-3, pi, e, sqrt(2), sin(), cos(), tan(), ln(), log(), abs(). Use * for multiplication.

Enter \(a\), \(b\), and \(h\), then click Calculate.

Trapezoid diagram (pan/zoom enabled)

Tip: zoom in to inspect the height and bases.

Rate this calculator

0.0 /5 (0 ratings)

Be the first to rate.

Your rating

Name (optional) Review (optional)

You can update your rating any time.

11. Trapezoid Area Calculator — Theory

A trapezoid is a quadrilateral with one pair of parallel sides. Those parallel sides are called the bases (lengths \(a\) and \(b\)). The height \(h\) is the perpendicular distance between the bases.

Area Formula

The area of a trapezoid is the average of the bases times the height:

\[ A=\frac{a+b}{2}\,h \]

Why the Formula Works

Imagine sliding two identical trapezoids together to form a parallelogram. The parallelogram has base \(a+b\) and height \(h\), so its area is \((a+b)h\). Since the parallelogram is made of two equal trapezoids, one trapezoid has half that area:

\[ A=\frac{(a+b)h}{2}=\frac{a+b}{2}\,h \]

Step-by-step Method

Compute the average base: \(\displaystyle m=\frac{a+b}{2}\).
Multiply by the height: \(\displaystyle A=m\,h\).

Worked Example

Bases \(a=6\text{ cm}\), \(b=10\text{ cm}\), height \(h=5\text{ cm}\).

\[ A=\frac{6+10}{2}\cdot 5=\frac{16}{2}\cdot 5=8\cdot 5=40\text{ cm}^2 \]

Common Mistakes

Using a slanted side as height: height must be perpendicular to the bases.
Forgetting the “/2”: the average base is \((a+b)/2\), not \((a+b)\).
Unit mismatch: if \(a,b,h\) are in cm, area is in \(\text{cm}^2\).

Solving for a Missing Value

If you know the area and want a missing base or height:

\(\displaystyle h=\frac{2A}{a+b}\)
\(\displaystyle a= \frac{2A}{h}-b\)
\(\displaystyle b= \frac{2A}{h}-a\)

Tip: The diagram in the calculator is a clean schematic (drawn as an isosceles trapezoid), but the area formula is valid for any trapezoid as long as \(a\) and \(b\) are the parallel sides and \(h\) is the perpendicular distance.

Frequently Asked Questions

What is the formula for the area of a trapezoid?

The area is A = (a + b)/2 x h, where a and b are the lengths of the parallel bases and h is the perpendicular height between them.

What is the height of a trapezoid and how is it different from a side length?

The height is the perpendicular distance between the two parallel bases. A slanted side is not the height unless it is perpendicular to the bases.

Does the trapezoid area formula work for any trapezoid?

Yes, the formula works for any trapezoid as long as a and b are the parallel sides and h is measured perpendicular to them.

What units will the trapezoid area be in?

If the inputs are in a length unit (for example cm), the area is reported in square units (cm^2). Keep a, b, and h in the same unit.

Rate this calculator

Frequently Asked Questions

Related calculators