Trapezoid Area Calculator
Area of a trapezoid from its two parallel sides and height.
Input sheet
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A trapezoid has two parallel sides of different lengths, and its area depends on both of them plus the perpendicular height. This calculator handles the standard formula instantly, which is handy for land plots, roof sections, and engineering cross-sections.
How it works
Trapezoid area = ½ × (base a + base b) × height, where a and b are the two parallel sides.
The trick to a trapezoid is that you average its two parallel sides to get the length of an "equivalent" rectangle, then multiply by the height. Because one base is shorter and one is longer, the average lands exactly in between and accounts for the slanted sides perfectly.
The height must be the perpendicular distance between the two parallel sides — not the length of a slanted side. Using a slanted edge by mistake overstates the area, since the true vertical gap is shorter than any leaning side.
Area = ½ × (base a + base b) × height, where base a and base b are the two parallel sides and height is the perpendicular distance between them.
Worked examples
Bases of 8 and 12 with a height of 5. → 50.00 sq units
(8 + 12) ÷ 2 = 10, and 10 × 5 = 50.
Bases of 6 and 10 with a height of 4. → 32.00 sq units
(6 + 10) ÷ 2 = 8, and 8 × 4 = 32.
Tips & gotchas
- Always use the perpendicular height between the parallel sides — never a slanted side length — or the area will come out too large.
- Keep both bases and the height in the same unit; mixing feet and inches silently corrupts the result.
- If both parallel sides are equal, the trapezoid is really a rectangle (or parallelogram) and the formula still gives the correct base × height.
- It doesn't matter which parallel side you call base a versus base b — addition is symmetric, so the area is the same.
FAQ
Which two sides are the bases?
The bases are the two parallel sides. The other two sides (the legs) aren't used directly in the area formula.
What if I only know a slanted side, not the height?
You need the perpendicular height. If you only have a slanted leg and an angle, find the height first with trigonometry before using this formula.
Does it matter which base I enter first?
No. The formula adds the two bases, so swapping base a and base b gives the identical area.
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