Enter the two parallel bases and the height to get the area of a trapezoid, plus its perimeter, median (midsegment), legs, diagonals and angles, drawn to scale. Switch modes to find a missing base or height from the area, or work out everything from all four sides.
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Find
Legs (sides)
Enter your values to see the result.
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How to use the Trapezoid Area Calculator
Choose what to find: area and perimeter, a missing base or a missing height.
Pick the leg type: isosceles, right trapezoid, or enter both legs yourself.
Enter the bases, height or area the mode asks for, and an optional unit.
Read the result with the perimeter, median, diagonals and angles.
Check the drawing and the steps, then copy the results.
Trapezoid formulas
Find
Formula
Example: a = 6, b = 10, h = 4 (isosceles)
Area
A = ½(a + b) × h
½ × 16 × 4 = 32
Median (midsegment)
m = (a + b) ÷ 2
8
Missing base
b = 2A ÷ h − a
64 ÷ 4 − 6 = 10
Missing height
h = 2A ÷ (a + b)
64 ÷ 16 = 4
Isosceles leg
√(h² + ((b − a) ÷ 2)²)
√(16 + 4) ≈ 4.472
Perimeter
a + b + c + d
6 + 10 + 2 × 4.472 ≈ 24.944
Isosceles diagonal
√(h² + ((a + b) ÷ 2)²)
√(16 + 64) ≈ 8.944
Why the formula works
Put a copy of the trapezoid next to itself, turned upside down. The two copies form a parallelogram whose base is a + b and whose height is h, so its area is (a + b)h. The trapezoid is half of that: ½(a + b)h. Another way to see it: cut along a diagonal to get two triangles with areas ½ah and ½bh, which add to the same result.
Types of trapezoids
Isosceles trapezoid: equal legs, equal base angles and equal diagonals. It is symmetric about the line through the midpoints of the bases.
Right trapezoid: one leg is perpendicular to the bases, so that leg equals the height and two angles are 90°. Common in floor plans and garden beds.
Scalene trapezoid: legs of different lengths. Enter both legs to get the height and angles.
Measuring a real space? Measure the height straight across between the parallel sides, not along a slanted side. For irregular plots, split the shape into trapezoids and triangles and add the areas, or use the area calculator.
Frequently asked questions
What is the formula for the area of a trapezoid?
A = ½(a + b) × h, where a and b are the two parallel sides (bases) and h is the perpendicular distance between them. With bases 6 and 10 and height 4: A = ½ × 16 × 4 = 32 square units.
How do I find a missing base of a trapezoid?
Rearrange the area formula: b = 2A ÷ h − a. For an area of 50, a known base of 7 and a height of 5: b = 100 ÷ 5 − 7 = 13.
How do I find the height of a trapezoid from the area?
h = 2A ÷ (a + b). For an area of 32 with bases 6 and 10: h = 64 ÷ 16 = 4.
What is the median (midsegment) of a trapezoid?
It is the segment joining the midpoints of the two legs. It is parallel to the bases and its length is their average, (a + b) ÷ 2. The area equals the median times the height.
How do I find the perimeter of a trapezoid?
Add all four sides: P = a + b + c + d. If you only know the bases and height of an isosceles trapezoid, each leg is √(h² + ((b − a) ÷ 2)²). With bases 6 and 10 and height 4, each leg is √20 ≈ 4.472 and P ≈ 24.94.
Can I find the area from the four side lengths?
Yes, if the bases are different lengths. The two legs and the difference of the bases form a triangle, which fixes the height. For bases 5 and 12 and legs 6 and 7, the height is about 5.421 and the area about 46.08.
Is a trapezoid the same as a trapezium?
In the US a trapezoid has one pair of parallel sides; in British English that shape is called a trapezium. The area formula is the same.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.