Trapezoid Calculator
Calculate the area and midsegment (median) of a trapezoid from its two base lengths and height. Enter base A, base B, and height to get instant, precise results.
How It's Calculated
Formula
\text{Area} = \frac{a + b}{2} \times h
\text{Midsegment} = \frac{a + b}{2}A trapezoid is a four-sided shape with exactly one pair of parallel sides, called the bases (a and b). Its area depends on the length of both bases and the perpendicular height between them: average the two base lengths, then multiply by the height. That same average — (a + b) / 2 — is also the length of the trapezoid's midsegment (also called the median): the line segment connecting the midpoints of the two non-parallel sides. The midsegment is always parallel to both bases and exactly halfway between them, which is why it shares the same formula as the averaging step inside the area calculation. This calculator does not compute perimeter, since that requires the lengths of the two non-parallel sides (legs), which aren't collected as inputs here.
Worked Examples
Standard case: base A = 6, base B = 10, height = 4
- Average the two bases: (a + b) / 2 = (6 + 10) / 2 = 8 — this is the midsegment.
- Multiply by the height: Area = 8 × 4 = 32
Decimal inputs: base A = 3.5, base B = 6.5, height = 2.5
- Average the two bases: (a + b) / 2 = (3.5 + 6.5) / 2 = 5 — this is the midsegment.
- Multiply by the height: Area = 5 × 2.5 = 12.5
Frequently Asked Questions
What if both bases are equal?
When base A equals base B, the shape is a parallelogram (a rectangle if the sides are also perpendicular to the bases), and the formula still holds: the midsegment equals that shared base length, and the area equals base × height, matching the standard rectangle/parallelogram area formula.
Why doesn't this calculator compute perimeter?
Perimeter requires the lengths of all four sides, including the two non-parallel legs. Base length and height alone don't determine the legs' lengths — the same two bases and height can be arranged into trapezoids with different leg lengths. Since leg lengths aren't collected as inputs, perimeter is out of scope for this calculator.
What is the midsegment (median) of a trapezoid used for?
The midsegment connects the midpoints of the two legs and is always parallel to both bases, with a length equal to the average of the two base lengths. It's a useful reference line in geometry proofs and constructions, and it's mathematically identical to the averaging step used inside the area formula.
What happens if I enter zero or a negative value?
Base A, base B, and height must each be a positive number greater than zero. A trapezoid with a zero-length base or zero height isn't a valid two-dimensional shape, so those inputs are treated as invalid rather than producing a result.