What Is a Trapezoid Area Calculator?
A trapezoid (also called a trapezium in British English) is a four-sided shape with exactly one pair of parallel sides, called the bases. This calculator finds the enclosed area from the lengths of the two parallel bases (a and b) and the perpendicular height (h) between them. It works for any units — centimeters, inches, meters, feet — and the result is simply expressed in the corresponding square units.
How to Use It
Enter the length of the first parallel side (base a), the length of the second parallel side (base b), and the height h, which is the perpendicular distance between the two bases. The calculator instantly returns the area along with the midsegment, which is the average length of the two bases.
The Formula Explained
The area of a trapezoid is given by:
$$A = \frac{a + b}{2} \times h$$
The expression \(\frac{a + b}{2}\) is the average of the two parallel sides — also known as the midsegment or median. Multiplying this average width by the height gives the area, exactly as you would for a rectangle whose width equals the average base length.
Worked Example
Suppose a trapezoid has bases \(a = 8\) and \(b = 5\) with a height \(h = 4\). First average the bases: $$\frac{8 + 5}{2} = 6.5.$$ Then multiply by the height: $$6.5 \times 4 = 26.$$ The area is therefore 26 square units.
Square Unit Conversions
Once you have computed a trapezoid's area with \(A = \frac{(a + b)}{2} \times h\), you often need to express the result in a different square unit. The table below lists exact and standard conversion factors between the most common units of area. Values marked as exact follow directly from the definitions of the units (for example, 1 inch is defined as exactly 2.54 cm, so 1 in² = 2.54² cm² = 6.4516 cm²); rounded factors are noted as approximate.
| From | To | Multiply by | Exact? |
|---|---|---|---|
| 1 m² | cm² | 10,000 | Exact |
| 1 m² | mm² | 1,000,000 | Exact |
| 1 cm² | mm² | 100 | Exact |
| 1 ft² | in² | 144 | Exact |
| 1 yd² | ft² | 9 | Exact |
| 1 in² | cm² | 6.4516 | Exact |
| 1 ft² | m² | 0.09290304 | Exact |
| 1 m² | ft² | 10.7639 | Approx. |
| 1 m² | in² | 1,550.0031 | Approx. |
| 1 acre | ft² | 43,560 | Exact |
| 1 acre | m² | 4,046.8564224 | Exact |
| 1 hectare | m² | 10,000 | Exact |
| 1 km² | m² | 1,000,000 | Exact |
| 1 mi² | acre | 640 | Exact |
Worked example. Suppose a trapezoidal garden bed has bases \(a = 5\) m and \(b = 3\) m and height \(h = 2\) m. Its area is
$$A = \frac{5 + 3}{2} \times 2 = \frac{8}{2} \times 2 = 4 \times 2 = 8 \text{ m}^2.$$That result of 8 m² converts to 86.11 ft² (using 1 m² = 10.7639 ft²), or equivalently 80,000 cm².
FAQ
Does it matter which base I call a or b? No. Because the formula adds a and b together, swapping them gives the same result.
What is the height exactly? The height is the perpendicular (shortest) distance between the two parallel bases — not the length of a slanted side.
Can I use different units for each side? No. All three measurements must be in the same unit, and the area comes out in that unit squared.
