Trapezoid Area Calculator
Compute trapezoid area A = (a + b) ÷ 2 × h — from parallel sides + height, or from 4 sides. Includes unit conversion, perimeter, diagram, and steps.
1. Choose mode & enter data
2. Worked examples (verified)
Example 1 — Basic formula
a = 10 cm, b = 14 cm, h = 6 cm.
Area = (10 + 14) ÷ 2 × 6 = 12 × 6 = 72 cm². Midsegment = (10 + 14) ÷ 2 = 12 cm.
Example 2 — Inch units + conversion
a = 8 in, b = 12 in, h = 5 in.
Area = (8 + 12) ÷ 2 × 5 = 50 in² = 322.58 cm² = 0.032258 m².
Example 3 — Given 4 sides (isosceles trapezoid)
a = 20, b = 12, c = 5, d = 5.
Base difference e = 8; projection x = (64 + 25 − 25) ÷ 16 = 4; height h = √(25 − 16) = 3.
Area = (20 + 12) ÷ 2 × 3 = 48 square units; perimeter = 20 + 12 + 5 + 5 = 42 units.
Example 4 — cm to m²
a = 200 cm, b = 300 cm, h = 150 cm.
Area = (200 + 300) ÷ 2 × 150 = 37,500 cm² = 3.75 m².
3. Frequently asked questions (FAQ)
What is the trapezoid area formula?
Trapezoid area = (a + b) ÷ 2 × h, where a and b are the two parallel sides and h is the height (the perpendicular distance between them). Example: a = 10 cm, b = 14 cm, h = 6 cm → area = (10 + 14) ÷ 2 × 6 = 72 cm².
What are the parallel sides a and b?
A trapezoid is defined by a pair of parallel sides, usually called base a (bottom) and base b (top). The order does not matter for area because the formula is symmetric: (a + b) ÷ 2 is the midsegment length.
What if only 4 sides are known without the height?
The height can be derived from the trapezoid legs. Let base difference e = a − b; then the projection of leg c onto the base is x = (e² + c² − d²) ÷ (2e), and height h = √(c² − x²). Example: a = 20, b = 12, c = 5, d = 5 → e = 8, x = 4, h = 3, area = 48 square units.
Does this formula work for isosceles and right trapezoids?
Yes. The formula (a + b) ÷ 2 × h works for all trapezoid types — isosceles, right, or scalene — because it only depends on the two parallel sides and the perpendicular distance between them.
How do you convert area result units?
This calculator accepts cm, m, in (inches), and ft (feet), then shows area in cm², m², in², and ft² at once. Reference: 1 in = 2.54 cm; 1 ft = 30.48 cm; 1 in² = 6.4516 cm²; 1 ft² = 929.0304 cm².
What is the midsegment of a trapezoid?
The midsegment (median) of a trapezoid is the segment connecting the midpoints of the two legs; its length = (a + b) ÷ 2 and it is parallel to the bases. Trapezoid area can also be written as midsegment × height. Example: a = 10, b = 14 → midsegment = 12.
What is the area of a trapezoid with a = 10, b = 14, and h = 6?
Area = (10 + 14) ÷ 2 × 6 = 12 × 6 = 72 square units (e.g. 72 cm² if the unit is cm).
Can this calculator compute trapezoid perimeter?
Yes, in 4-side mode the perimeter is computed automatically as a + b + c + d. Example: sides 20, 12, 5, 5 → perimeter = 42 units.
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