A trapezoid (also called a trapezium) is a four-sided shape with exactly one pair of parallel sides. The two parallel sides are labelled a and b, the perpendicular height between them is h, and the two sloping sides that connect them are the legs c and d. This calculator takes those five measurements and returns the three most useful properties: the area, the median (also called the midsegment), and the perimeter. The area is the most commonly needed result, and it follows a simple formula: average the two parallel sides and multiply by the height, giving Area = 0.5 x (a + b) x h. You can think of this as turning the trapezoid into an equivalent rectangle with width equal to the median and height h. The median is the line drawn midway between the parallel sides, connecting the midpoints of the two legs. Its length is always the arithmetic average of the two parallel sides: Median = (a + b) / 2. The perimeter is simply the sum of all four sides: a + b + c + d. You need both leg lengths to calculate the perimeter; if you only have the parallel sides and the height you can still get the area and the median. Choose a unit, enter the values, and the results update instantly. The area is shown with the squared unit, and the median and perimeter use the linear unit. This calculator is suited to students working on geometry homework, builders measuring angled panels or pitched roofs, and landscapers designing trapezoidal garden beds. All inputs must be positive. The calculator treats h as the perpendicular height, not the length of a sloping side.
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26.00 m²
area
Median (midsegment)6.50 m
Perimeter22.00 m
Height h must be the perpendicular distance between the two parallel sides, not the length of a sloping leg. Enter both legs c and d for the perimeter; without them it shows "need both legs".
How it works
The area of a trapezoid uses the formula: Area = 0.5 x (a + b) x h. The median (midsegment) is the average of the two parallel sides: Median = (a + b) / 2. Multiplying median by height gives the area, which is a useful cross-check. The perimeter adds all four sides: Perimeter = a + b + c + d. If either leg is missing, the perimeter cannot be computed. All values must be positive numbers in the same unit.
Worked example
A trapezoid has parallel sides a = 8 and b = 5, perpendicular height h = 4, leg c = 4, and leg d = 5. Area = 0.5 x (8 + 5) x 4 = 0.5 x 13 x 4 = 26.00. Median = (8 + 5) / 2 = 6.50. Perimeter = 8 + 5 + 4 + 5 = 22.00. These are the default values pre-filled in the calculator above.
