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Trapezoid Area Calculator – Bases, Height & Median Formula

Geometry Math area calculator geometry trapezoid
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Input Parameters
m
Please enter a positive number.
m
Please enter a positive number.
m
Please enter a positive number.
Formula
Area = (a + b) × h ÷ 2
Median m = (a + b) ÷ 2  |  Area = m × h
Result
Area
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square meters (m²)
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Base 1 (a)
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Base 2 (b)
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Height (h)
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Median (m)
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Sum of Bases
h a = 8 b = 12 m

Frequently Asked Questions

What is the formula for the area of a trapezoid?
The area of a trapezoid is calculated using the formula: Area = (a + b) × h ÷ 2, where a and b are the lengths of the two parallel bases, and h is the perpendicular height between them. Alternatively, you can use the median (midsegment) formula: Area = m × h, where m = (a + b) ÷ 2.
What is the median (midsegment) of a trapezoid?
The median (also called the midsegment) of a trapezoid is the line segment that connects the midpoints of the two non-parallel sides (legs). Its length equals the average of the two bases: m = (a + b) ÷ 2. The median is always parallel to both bases, and the area can be found by multiplying the median by the height.
How do I find the height if I know the area and bases?
Rearrange the area formula to solve for height: h = 2 × Area ÷ (a + b). Simply multiply the area by 2, then divide by the sum of the two bases. Make sure all measurements use the same unit.
Can a trapezoid have equal bases?
Yes! If both bases are equal (a = b), the trapezoid becomes a parallelogram. In that case, the area formula simplifies to Area = a × h (since (a+a)×h÷2 = a×h), which is the same as the parallelogram area formula. If the legs are also perpendicular to the bases, it becomes a rectangle.
What are some real-world applications of trapezoid area calculations?
Trapezoid area calculations are used in: construction & roofing (gable ends, irregular lots), civil engineering (canal cross-sections, road embankments), land surveying (irregular property boundaries), architecture (trapezoidal windows, awnings), manufacturing (sheet metal cutting), and mathematics education.
How accurate is this trapezoid area calculator?
This calculator uses standard double-precision floating-point arithmetic and displays results rounded to 4 decimal places. For most practical purposes (construction, homework, engineering estimates), this precision is more than sufficient. Input validation ensures all values are positive before calculation.
Does the order of Base 1 and Base 2 matter?
No, the order does not affect the area calculation because addition is commutative: (a + b) = (b + a). You can label either parallel side as Base 1 or Base 2. In our diagram, Base 1 is shown as the top base and Base 2 as the bottom base for visual clarity.
What units should I use with this calculator?
You can use any unit of length (inches, feet, yards, centimeters, meters, etc.) as long as all inputs use the same unit. The area result will be in square units of your chosen measurement (e.g., if you input meters, the result is in square meters). Use the unit selector dropdown to label your units appropriately.
How is the perimeter of a trapezoid calculated?
The perimeter of a trapezoid is the sum of all four sides: P = a + b + c + d, where c and d are the lengths of the two non-parallel legs. Note: this calculator focuses on area; to compute the full perimeter you would need the leg lengths, which are not required for area calculation.
What is the difference between a trapezoid and a trapezium?
In US English, a trapezoid is a quadrilateral with at least one pair of parallel sides. In UK English, this shape is called a trapezium, while a trapezoid in the UK refers to a quadrilateral with no parallel sides. This calculator follows the US convention.
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