Trapezoid Area

What the Trapezoid Area Calculator Does

This calculator finds the area of a trapezoid from its two parallel sides and the perpendicular height between them. A trapezoid (called a trapezium in British English) is a four-sided shape with exactly one pair of parallel sides. Those parallel sides are usually labeled a and b, and the distance between them is the height, h.

It is built for students checking geometry homework, teachers preparing worksheets, and anyone working with real shapes: a section of land, a roof gable, a piece of sheet metal, or a garden bed. Enter the two parallel sides and the height in the same unit, and the result comes back in square units.

How It Works: The Trapezoid Area Formula

The trapezoid area formula is:

area = ((a + b) / 2) * h

Here a and b are the lengths of the two parallel sides, and h is the perpendicular height (the shortest, straight-up distance between the parallel sides, meeting them at a right angle). The term (a + b) / 2 is simply the average of the two parallel sides, so a trapezoid has the same area as a rectangle whose width equals that average and whose length equals the height.

All three inputs must use the same unit before you calculate. The answer is always in that unit squared, for example square meters or square inches.

Worked Example With Real Numbers

Suppose a trapezoid has parallel sides of a = 8 cm and b = 12 cm, with a perpendicular height of h = 5 cm.

Add the parallel sides: 8 + 12 = 20. Divide by 2 to get the average: 20 / 2 = 10 cm. Multiply by the height: 10 * 5 = 50. The area is 50 square centimeters (cm squared).

As a check, the average side (10 cm) lies between the two parallel sides (8 and 12), which it always should. If your average falls outside that range, you have made an arithmetic slip.

Common Mistakes and Factors That Affect the Result

The most frequent error is using a slanted side instead of the true perpendicular height. The slant (the non-parallel edge) is longer than h and will overstate the area. Height must be measured at a right angle to the parallel sides.

A few other things to watch for:

• Mixed units: convert everything to one unit first (e.g., do not mix cm and mm).
• Wrong sides chosen: only the two parallel sides go in as a and b, not the slanted ones.
• Right trapezoids: if one side is vertical, that vertical side equals the height. Confirm it is actually perpendicular.
• Rounding: round only the final answer, not the intermediate steps, to avoid drift.

Tips and Related Calculations

If you only know the slant side and an angle, find the height first with trigonometry (h = slant * sin(angle)), then apply the formula. If you know the area and want a missing side, rearrange it: a = (2 * area / h) - b.

The formula works for any trapezoid, including right and isosceles ones, because it depends only on the parallel sides and the perpendicular distance, not on the shape's symmetry. For a parallelogram, where both pairs of sides are parallel and equal, a equals b, so the formula reduces to base times height.