Trapezoid Area Calculator
A trapezoid with bases 8 and 12 and a perpendicular height of 5 has an area of 50 square units. This trapezoid area calculator helps you find that result fast by averaging the two parallel sides and multiplying by the true height between them. Enter base a, base b, and height to get the area plus the median length, which is the same average of the two bases. This page is useful when you are checking geometry homework, estimating a tapered garden bed, measuring a roof end, or turning a sketch into a clean area figure for planning. The key idea is simple. A trapezoid does not keep the same width from top to bottom, so the formula replaces that changing width with its average. Once you understand that average width, the area works just like a rectangle. The most common mistake is using a slanted side instead of the perpendicular height. If the distance between the bases is not measured at a right angle, the area will be wrong. The worked examples below show how to spot the correct inputs and how the median helps you sanity-check the answer.
Quick answer
A trapezoid has one pair of parallel sides, and those parallel sides are the only side lengths used as bases in the area formula.
Area
50
Median length
10
What this tells you
- •A trapezoid has one pair of parallel sides, and those parallel sides are the only side lengths used as bases in the area formula.
- •Its area equals the average of the two bases times the perpendicular height between them.
- •The same average of the bases is also the trapezoid's median or midsegment length, so the area can be seen as median times height.
- •If both bases are equal, the trapezoid becomes a parallelogram and the formula reduces to base times height.
- •Swapping base a and base b does not change the answer because the formula depends on their sum, not their order.
- •Units matter. If the bases are in feet and the height is in feet, the result is in square feet.
How to Use
- 11. Enter the length of the first parallel side in Base a. Any positive decimal is fine.
- 22. Enter the length of the second parallel side in Base b. The larger base does not need to go first.
- 33. Enter the perpendicular height, which is the shortest straight-line distance between the two bases.
- 44. Read the area result. The tool also shows the median length, which should equal the average of the two bases.
- 55. If a drawing gives you a slanted leg instead of the height, derive the true height before using the calculator.
- 66. Keep the input units consistent. Mixing inches with feet or centimeters with meters will distort the area.
How It Works
Formula
A = (a + b) / 2 x hIn this formula, a and b are the lengths of the parallel sides and h is the perpendicular height between them. First add the two bases, then divide by 2 to find their average. That average is the trapezoid's median length. Multiply the average by the height to get area. Using the tool's default values shows the process clearly. For bases 8 and 12, the average is (8 + 12) / 2 = 10. Multiply 10 by height 5 and the area is 50 square units. The formula works because two matching trapezoids can be arranged into a parallelogram with base a + b and the same height. One trapezoid is half of that parallelogram, so its area is ((a + b) x h) / 2.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Bases 8 and 12 with height 5
Add the bases to get 20, then divide by 2 to get a median of 10. Multiply 10 by the height of 5 to get an area of 50. This is the clean textbook case and a good quick check for the calculator's default values.
Garden bed with bases 4 m and 2.5 m and height 6 m
The average of the two parallel sides is (4 + 2.5) / 2 = 3.25 meters. Multiply 3.25 by 6 to get 19.5 square meters. This kind of example comes up when a planting bed widens or narrows evenly from one end to the other.
Roof end with bases 30 ft and 18 ft and height 9 ft
Average the bases first: (30 + 18) / 2 = 24 feet. Then multiply 24 by the 9-foot height to get 216 square feet. For estimating siding or sheathing on a trapezoidal section, this area is the number you would price against before waste allowances.
Classroom sketch with bases 15 cm and 9 cm and height 7 cm
The base average is (15 + 9) / 2 = 12 centimeters. Multiply 12 by 7 to get 84 square centimeters. Because the median is 12, you can also picture an equivalent rectangle that is 12 by 7.
Tapered concrete section with bases 22 in and 14 in and height 11 in
Adding the bases gives 36 inches, and dividing by 2 gives a median of 18 inches. Multiply 18 by 11 to get 198 square inches. This is a useful pattern when a section drawing shows a top width and bottom width with a vertical depth between them.
Common trapezoid area checks
These examples use the same formula as the calculator and give you quick benchmark values for homework, sketches, and estimate reviews.
| Base a | Base b | Height | Median | Area |
|---|---|---|---|---|
| 4 | 6 | 3 | 5 | 15 |
| 8 | 12 | 5 | 10 | 50 |
| 10 | 14 | 8 | 12 | 96 |
| 5 | 9 | 4 | 7 | 28 |
| 20 | 30 | 10 | 25 | 250 |
When the trapezoid formula is most useful
The trapezoid area formula is most useful when a shape has two parallel sides but does not keep a constant width from top to bottom. That happens often in geometry assignments, landscape layouts, roof profiles, cross sections, ramps, and any plan where one edge is longer than the opposite edge.
A good mental shortcut is to think about the median first. The median tells you the shape's average width. Once you know that value, the trapezoid behaves like a rectangle with that average width and the same height. This makes it easier to estimate, check a diagram, or catch a typing error before you rely on the result.
Common mistakes
- Using a slanted leg as the height. The height must be the perpendicular gap between the two parallel bases.
- Choosing the wrong pair of sides as the bases. Only the parallel sides belong in a and b.
- Adding the bases and multiplying by height without dividing by 2. That doubles the real area.
- Mixing units, such as entering bases in inches and height in feet. Convert first so every input uses the same unit.
- Forgetting that the result is square units. A 50-foot result should be written as 50 square feet, not 50 feet.
- Rounding too early during hand calculation. Keep the base average and height precise until the final step.
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