The Area Of A Trapezoid Calculator
A trapezoid has two parallel sides of different lengths, and its area is the average of those two sides multiplied by the distance between them.
Area of the trapezoid
32
- Median
- 8
- Leg length if symmetric
- 4.4721
- Perimeter if symmetric
- 24.9443
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
A = (a + b) / 2 x h
- a
- Length of the first parallel side
- b
- Length of the second parallel side
- h
- Perpendicular height between the two parallel sides
- A
- Area enclosed by the trapezoid
How to check the result by hand
- 1
Identify the two parallel sides
A trapezoid has exactly one pair of parallel sides, and the formula uses those two and only those two. If you are unsure which are parallel, check the shape against a straight edge or look for the two sides that never meet.
- 2
Add them together
Sum the two parallel lengths. For sides of 6 and 10 the total is 16. Adding is safe regardless of which is longer, so the order does not matter.
- 3
Halve the total to get the median
16 divided by 2 is 8. This median is the width of the shape at its midpoint, and it is the single number that replaces the two bases in the rest of the calculation.
- 4
Multiply by the perpendicular height
8 times a height of 4 gives 32 square units. Use the perpendicular gap between the bases, not the length of a slanted leg, or the answer will come out too large.
- 5
Add the legs if you need the perimeter
For an isosceles trapezoid the legs are equal, so the perimeter is the two parallel sides plus twice one leg. Work out the leg from the height and half the difference between the bases when it has not been measured directly.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate The Area Of A Trapezoid page.