Everyday utility

Trapezoid Calculator

Enter the two parallel sides, the perpendicular height, and the two non-parallel legs to calculate area and perimeter. The height must be the perpendicular distance between the parallel sides, not the slanted leg length.

Last reviewed May 19, 2026 by ToolSpilo Editorial Team.

Review method: Reviewed against standard trapezoid geometry formulas and height derivation.

Calculator tool

How this calculator works

Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.

What a Trapezoid Is

A trapezoid (also called a trapezium outside North America) is a four-sided shape with exactly one pair of parallel sides. The two parallel sides are called the bases. The other two sides are called the legs.

Formulas

Let aa and bb be the two parallel sides, hh the perpendicular height, and cc and dd the two legs.

MeasurementFormula
AreaA=(a+b)2×hA = \dfrac{(a + b)}{2} \times h
PerimeterP=a+b+c+dP = a + b + c + d

Worked Example

For a trapezoid with parallel sides 10 m and 6 m, perpendicular height 4 m, and legs 4.5 m each:

A=(10+6)2×4=8×4=32 m2A = \frac{(10 + 6)}{2} \times 4 = 8 \times 4 = 32\text{ m}^2
P=10+6+4.5+4.5=25 mP = 10 + 6 + 4.5 + 4.5 = 25\text{ m}

Why the Perpendicular Height Matters

The area formula requires the perpendicular height — the shortest distance between the two parallel sides measured at 90°. If you use the slant length of a leg instead, the area will be overstated. In most problems the perpendicular height is given or marked with a small square symbol.

Common Uses

Trapezoid area calculations appear in construction (sloped rooflines, retaining walls), land measurement (irregular land plots), bridge cross-sections, and dam spillways.

Frequently asked questions

How do I find the height of a trapezoid if it is not given?

If the leg length and horizontal offset are known, the height follows from the Pythagorean theorem. For a right trapezoid where one leg is vertical, that vertical leg is the height. For an isosceles trapezoid with leg cc and parallel sides a>ba > b, the height is:

h=c2−(a−b2)2h = \sqrt{c^2 - \left(\frac{a - b}{2}\right)^2}

For example, if a=10a = 10, b=6b = 6, and c=5c = 5, then h=25−4=21≈4.58 mh = \sqrt{25 - 4} = \sqrt{21} \approx 4.58\text{ m}.

What is the difference between a trapezoid and a parallelogram?

A parallelogram has two pairs of parallel sides, and opposite sides are equal. A trapezoid has only one pair of parallel sides. A rectangle, square, and rhombus are all special parallelograms. A parallelogram's area is base × height; a trapezoid's area also uses height but averages the two unequal bases first.

Does the order of the parallel sides (a and b) affect the result?

No. The area formula adds aa and bb symmetrically, so swapping them gives the same result. For a trapezoid with bases 10 and 6: (10+6)/2=8(10 + 6)/2 = 8, and (6+10)/2=8(6 + 10)/2 = 8. Only the height and the sum of the bases affect the area.

What is an isosceles trapezoid?

An isosceles trapezoid is a trapezoid where the two non-parallel legs are equal in length. This gives the shape a line of symmetry through the midpoints of the parallel sides. The base angles on each side are also equal. Many standard trapezoid problems assume an isosceles shape.