Trapezoid Area Calculator
Find the area of a trapezoid from its two parallel sides and the perpendicular height, plus the length of its median.
How it works
Area = ½ · (a + b) · h · Median = (a + b) ÷ 2
A trapezoid has one pair of parallel sides, called the bases. Its area is the average of the two base lengths times the perpendicular height — averaging the bases turns the sloped shape into an equivalent rectangle. That average, (a + b) ÷ 2, is also the length of the median: the segment joining the midpoints of the two non-parallel sides, which always runs parallel to the bases.
Worked example
With parallel sides a = 8 and b = 5 and height h = 4: the median is (8 + 5) ÷ 2 = 6.5, and the area is ½ × (8 + 5) × 4 = ½ × 13 × 4 = 26 square units. You can read the area as the median 6.5 multiplied by the height 4, which also gives 26.
Sources: Trapezoid — Wikipedia
Frequently asked questions
Which measurement is the height?
The height is the perpendicular (straight-across) distance between the two parallel sides, not the length of a slanted leg. If you only know a slanted side and its angle, find the height first as side × sin(angle).
What is the median of a trapezoid?
The median, or midsegment, connects the midpoints of the two non-parallel sides. Its length equals the average of the two bases, (a + b) ÷ 2, and it is always parallel to them. Area equals the median times the height.
Does it matter which base is a and which is b?
No. The formula adds the two bases, so swapping a and b gives the same sum and the same area. Only the height must be measured correctly, perpendicular to both bases.
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This calculator is for educational purposes. Double-check important results before acting on them.