What is the area formula for a trapezoid?

Area equals one-half times the sum of the two parallel bases times the height (A = 1/2 · (a + b) · h).

What is the midsegment of a trapezoid?

The midsegment, or median, equals the average of the two parallel bases, (a + b) / 2.

Why do the legs only change the perimeter?

The area depends only on the two parallel bases and the height. The legs affect the perimeter but not the enclosed area.

What is the difference between a trapezoid and a trapezium?

They are the same four-sided shape with one pair of parallel sides. Trapezoid is the US term and trapezium the British term; this calculator works for either name.

How is the perimeter calculated?

The perimeter is the sum of all four sides: the two parallel bases plus the two legs (a + b + c + d).

Does the height have to be perpendicular?

Yes. The height is the perpendicular distance between the two parallel bases, not the length of a slanted leg, since the area formula relies on the perpendicular height.

Yes, as long as all lengths use the same unit. The area then comes out in that unit squared and the perimeter and midsegment in the same linear unit.

Trapezoid Calculator

Trapezoid calculator

A trapezoid (British: trapezium) is a four-sided shape with one pair of parallel sides, called the bases. This calculator finds its area, midsegment, and perimeter from the bases, the height, and the two legs — useful for geometry homework, construction layouts, and land-area estimates.

How it works

Let the parallel bases be a and b, the perpendicular height be h, and the two slanted legs be c and d:

Area       = ½ × (a + b) × h
Midsegment = (a + b) / 2
Perimeter  = a + b + c + d

The area and midsegment depend only on the bases and height; the legs affect only the perimeter. Note that h must be the perpendicular distance between the bases, not the length of a leg.

Example

For bases a = 8 and b = 12, height h = 5, and legs c = 6, d = 7:

Area = ½ × (8 + 12) × 5 = ½ × 20 × 5 = 50
Midsegment = (8 + 12) / 2 = 10
Perimeter = 8 + 12 + 6 + 7 = 33

Quantity	Value
Area	50
Midsegment	10
Perimeter	33

Works for any trapezoid and updates instantly in your browser, with nothing uploaded.