How to Find the Area of a Trapezoid

The formula

A trapezoid has exactly one pair of parallel sides. Those two are the ones the formula cares about, and they are usually labelled a and b.

A = ((a + b) ÷ 2) × h

In words: average the two parallel sides, then multiply by the height. The height is the perpendicular distance between the parallel sides — straight across, at a right angle. It is not the length of the slanted side, and mixing those up is the single most common trapezoid error.

A worked example

Take a trapezoid with parallel sides of 10 and 6, and a height of 4.

Average the parallel sides: (10 + 6) ÷ 2 = 8.

Multiply by the height: 8 × 4 = 32 square units.

That is the example loaded into the calculator on this page, so you can change the numbers and watch each step update.

Why averaging the sides works

This formula is easier to remember once you see where it comes from, and the reason is quite satisfying.

Imagine taking a second copy of your trapezoid, turning it upside down, and pushing it against the first. The two fit together into a parallelogram — because the slanted sides match up exactly.

That parallelogram has a base of (a + b) and the same height h, so its area is (a + b) × h. But it is made of two trapezoids, so one trapezoid is half of that: ((a + b) ÷ 2) × h.

The average in the formula is doing the work of that "divide by two". You are effectively finding the width of the trapezoid halfway up, where it is exactly the average of its top and bottom.

Finding the perimeter as well

The area formula only needs three measurements, but the perimeter needs all four sides — the two parallel ones plus the two slanted legs.

Perimeter is simply a + b + c + d, adding them all up. The calculator asks for the legs too, so it can give you both numbers at once.

If you only know the parallel sides and the height, you cannot find the perimeter without more information. That is not a limitation of the calculator; there are genuinely many different trapezoids with the same area and different perimeters.

Getting the height right

If your trapezoid is drawn with a slanted leg and you have been given that leg's length rather than the height, you will need to find the height first.

For a right trapezoid — one where a leg meets the parallel sides at 90° — that leg is the height, and there is nothing to do.

Otherwise, drop a perpendicular from the end of the shorter parallel side down to the longer one. That creates a right triangle whose hypotenuse is the slanted leg, and Pythagoras will give you the height from there.

Where this comes up outside homework

Trapezoids turn up more often in practical work than most shapes. Garden beds and patios frequently end up trapezoidal when a boundary is not square. Roof sections, particularly on hipped roofs, are usually trapezoids. So are the cross-sections of drainage channels and canals.

In each case, the measurement to be careful about is the same one: get the perpendicular height, not the slope length, or your material estimate will come out short.