# Area of a Trapezium

The area of a trapezium, also known as trapezoid, is ½(a + b) h. This article shows how to calculate the area and rearrange the formula to find the sides given the area.

## Formula

This is the standard formula to calculate the area A when given, a, b, and h. A Physicist usually calculates the area of a trapezoidal prism using this formula.

## Derivation

Calculating the area is simple using the standard formula, but sometimes you might be given the area, and will need to calculate the height, or solve for a, or b.

In order to derive the values of a, b, and h, you will need to learn to transpose the standard formula for area. It is very easy to transpose and it is worth learning a little bit of algebra for this. The expressions shown above were derived using algebra.

Shown above are three formulas to solve for h, a, and b. This is useful if height is not given, or any one of the sides is not given.

## Calculator Solver

Area A:

Height h:

a:

b:

Solve for A:

Solve for h:

Solve for a:

Solve for b:

Here is a calculator solver to find out the area of a trapezoid online. There are four calculators to calculate any of the unknown parameters in the standard formula. Make sure that your parameters are in the same units.