Trapezoid calculator — area, midsegment and perimeter (isosceles or not)

How to use the trapezoid calculator

1. Enter Parallel side a and Parallel side b, the two sides that run parallel. Order does not matter.
2. Enter the Height, measured at right angles between them, not along a slanted side.
3. For an isosceles trapezoid, leave Leg c and Leg d at 0. Otherwise, enter both legs.
4. Read Area (½(a + b)h), Median (midsegment) and Perimeter. For the isosceles case you also get Each leg (isosceles).

What it does and when to use it

Trapezoids show up in sloping roofs, the side walls of a lean-to shed, ramps, embankments, the cross-section of a ditch or canal, and plots of land with one slanted boundary. The area tells you how much roofing, cladding or turf you need. The perimeter gives the length of trim or fencing. Students use the area formula a lot, and it is also the basis of the trapezium rule for estimating the area under a curve.

For a trapezoid as one choice among many shapes, the area calculator and perimeter calculator show the formula with your numbers. The Pythagorean calculator helps if you need a leg or the height from other measurements.

How it works

• Area: ½ × (a + b) × h
• Median (midsegment): (a + b) ÷ 2
• Perimeter: a + b + c + d
• Isosceles legs (when both are 0): each leg = √(((a − b) ÷ 2)² + h²). The longer base sticks out by (a − b) ÷ 2 on each side, which forms a right triangle with the height.

Worked examples

An isosceles trapezoid, step by step. a = 12, b = 8, height 5, legs left at 0.

1. Overhang on each side: (12 − 8) ÷ 2 = 2.
2. Leg: √(2² + 5²) = √29 = 5.385164807.
3. Area: ½ × (12 + 8) × 5 = 50.
4. Perimeter: 12 + 8 + 2 × 5.385164807 = 30.77032961.

The tool shows Each leg (isosceles): 5.385164807, a median of 10 and Perimeter: 30.77032961.

Unequal legs. a = 20, b = 6, height 12, legs 13 and 15. The area is Area (½(a + b)h): 156, the median 13 and the perimeter 54. These legs fit exactly: they stick out 5 and 9 units, which add up to 20 − 6 = 14.

Limits and tips

• Two legs you enter must fit together. Their horizontal overhangs, √(leg² − h²), must add up to the difference between the bases (both legs slope outwards) or differ by it (one leans over). If neither is true within 1% of the longer base, the tool says the legs do not fit instead of giving a perimeter for a shape that cannot exist.
• Fill in both legs or neither. One leg on its own gives a message.
• No unit menu: area is in your unit squared.
• Runs in your browser.