Trapezoid Area and Perimeter Calculator
Compute the area or perimeter of any trapezoid instantly. Enter both parallel bases and the height for area, or all four sides for perimeter — ideal for geometry homework and construction layouts.
About this calculator
A trapezoid is a quadrilateral with exactly one pair of parallel sides, called the bases. Its area is found by averaging the two bases and multiplying by the perpendicular height: Area = ((base1 + base2) × height) / 2. This formula works because a trapezoid can be seen as the average of two rectangles stacked together. The perimeter is simply the sum of all four sides: Perimeter = base1 + base2 + side1 + side2. These formulas apply to any trapezoid — right, isosceles, or scalene — as long as the height is the perpendicular distance between the two parallel bases, not the slant of a leg.
How to use
Suppose you have a trapezoid with a top base of 6 units, a bottom base of 10 units, a height of 4 units, and two slanted sides of 5 units each. For area: Area = ((6 + 10) × 4) / 2 = (16 × 4) / 2 = 64 / 2 = 32 square units. For perimeter: Perimeter = 6 + 10 + 5 + 5 = 26 units. Select 'Area' or 'Perimeter' in the Calculate field, enter your values, and the result appears immediately.
Frequently asked questions
What is the formula for the area of a trapezoid and why does it work?
The formula is Area = ((base1 + base2) × height) / 2. It works because a trapezoid is essentially an averaged rectangle — if you placed two identical trapezoids together, they would form a parallelogram with base (base1 + base2) and height h. Dividing by 2 gives the area of just one trapezoid. This makes the formula valid for all trapezoid types as long as height is the perpendicular distance between the parallel sides.
How do I find the perimeter of a trapezoid if I only know the bases and height?
If you only know the two bases and the height, you cannot determine the perimeter without additional information, because the slant lengths of the two non-parallel sides depend on how the trapezoid is oriented. For a right trapezoid or isosceles trapezoid, you can use the Pythagorean theorem to compute the leg lengths from the height and horizontal offset. Once you have all four side lengths, Perimeter = base1 + base2 + side1 + side2.
When should I use a trapezoid area calculator in real life?
Trapezoid area calculations appear frequently in construction, landscaping, and surveying whenever a plot or cross-section has one pair of parallel edges of different lengths. For example, calculating the square footage of a trapezoidal room, the cross-sectional area of a drainage channel, or the material needed for a trapezoidal roof panel. Having a quick calculator saves time and reduces arithmetic errors on the job site.