Trapezoid Area Calculator: Formula, Median and Step-by-Step Answer
Geometry & trigFreeNo sign-up
Enter the two parallel bases and the height.
A trapezoid with bases 10.0000 and 6.0000 cm and height 4.0000 cm has an area of 32.0000 cm². Its median (midsegment) is 8.0000 cm.
Show the steps
- Add the bases: 10.0000 + 6.0000 = 16.0000.
- Half of that is the median: 8.0000.
- Area = median × height = 8.0000 × 4.0000 = 32.0000 cm².
Trapezoid
A = ½ (a + b) h
Median = (a + b) ÷ 2
Perimeter = a + b + c + d
Estimates for planning and learning, not financial, tax, legal or medical advice. Check figures with your lender, tax preparer or doctor before you act.
About this calculator
A trapezoid (called a trapezium in some countries) is a four-sided shape with one pair of parallel sides, the bases. Its area is A = ½ (a + b) h: the average of the two bases times the height.
Enter the bases and the height. You get the area, the median (the line halfway between the bases), and the perimeter if you add the two legs.
How to use it
- Enter the lengths of the two parallel bases.
- Enter the height, the perpendicular distance between the bases.
- Optional: open the extra fields to add the two legs for the perimeter. Read the area and steps.
Trapezoid formulas
- Area: A = ½ (a + b) h
- Median: m = (a + b) ÷ 2, so A = m × h
- Perimeter: a + b + c + d
Example
Bases 10 and 6, height 4: A = ½ × (10 + 6) × 4 = 32 square units.
Why it works
A trapezoid is a rectangle of width equal to the shorter base, plus two triangles. Averaging the bases gives the same total area in one step.
Sources
Quick check: test yourself
A trapezoid has bases 6 and 5 and height 7. What is its area?
Correct answer: 38.5. A = ½ × (6 + 5) × 7 = 38.5.
Which formula gives the area of a trapezoid?
Correct answer: ½ (a + b) h. Average the two bases, then multiply by the height.
What is the median of a trapezoid with bases 10 and 6?
Correct answer: 8. (10 + 6) ÷ 2 = 8.
Pick an answer for each question.
Common questions
What is the formula for the area of a trapezoid?
A = ½ (a + b) h, where a and b are the parallel sides and h is the height.
Is the height the same as a leg?
Only in a right trapezoid. In general the height is the perpendicular distance between the bases, so it is shorter than a slanted leg.
What is the median of a trapezoid?
The segment joining the midpoints of the legs. Its length is the average of the bases.
Can the bases be equal?
Yes. Then the shape is a parallelogram and the formula gives base × height.
What is a trapezium?
In British English it means a trapezoid. In American English a trapezium is a shape with no parallel sides.
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