Trapezoid Calculator

How it works

A trapezoid has one pair of parallel sides, the bases, joined by two legs. Its area is the average of the two bases times the height, the perpendicular distance between them: the figure has the same area as a rectangle of that height whose width is the midsegment, the line joining the midpoints of the legs, which is exactly the average of the bases.

Four sides fix the shape as long as the bases differ. Slide one leg along the bases until the two legs meet: they form a triangle with the difference of the bases as its third side, and the height of the trapezoid is the height of that triangle, found here with Heron's formula. If the bases are equal the figure is a parallelogram and its height can be anything, so that case needs the height typed in.

When you give the bases and the height the legs stay unknown, so the perimeter is left blank. Give all four sides when you need edging, fencing or trim as well as area.

Formula

area       = (a + b) ÷ 2 × h
midsegment = (a + b) ÷ 2
perimeter  = a + b + c + d
h (from four sides, a ≠ b) = 2 × triangle area(|a − b|, c, d) ÷ |a − b|
                           = √(c² − ((a − b)² + c² − d²)² ÷ (4 (a − b)²))

Example

A trapezoid with bases 10 ft and 4 ft and legs of 5 ft each: the legs and the 6 ft base difference form a 6-5-5 triangle whose height is 4 ft, so the trapezoid is 4 ft high. Its area is (10 + 4) ÷ 2 × 4 = 28 ft², the midsegment is 7 ft, and the perimeter is 10 + 4 + 5 + 5 = 24 ft.

With bases 14 ft and 4 ft and legs 6 ft and 8 ft, the leg triangle is 10-6-8, a right triangle, whose height onto the 10 ft side is 6 × 8 ÷ 10 = 4.8 ft. The area is 9 × 4.8 = 43.2 ft² and the perimeter 32 ft.

Given only bases of 10 ft and 6 ft with a 4 ft height, the area is 8 × 4 = 32 ft², the midsegment is 8 ft, and the perimeter is left blank.

Assumptions and limitations

• Exactly one pair of sides is parallel (or both, for a parallelogram); the two bases are that pair.
• From four sides alone the height is only fixed when the bases differ. With equal bases, enter the height.
• The perimeter needs the legs, so it is blank when only the bases and height are given.
• All lengths are in the unit you chose. The calculator labels the results with it and does not convert between units.
• Results are rounded for display only.

Frequently asked questions