Geometry Tool
Trapezoid Calculator
Calculate area, perimeter, midsegment, and height of any trapezoid. Enter bases, height, and optional leg lengths with step-by-step formulas.
Area & Perimeter-Midsegment-Height from Legs-Isosceles Check
Trapezoid Calculator
Trapezoid Formulas
| Property | Formula | Variables |
|---|---|---|
| Area | A = (a + b) / 2 x h | a, b = bases; h = height |
| Perimeter | P = a + b + c + d | c, d = legs |
| Midsegment | m = (a + b) / 2 | Connects midpoints of legs |
| Height (from leg) | h = sqrt(leg^2 - ((b-a)/2)^2) | Isosceles trapezoid |
| Diagonal (approx) | d = sqrt(h^2 + (b-a)^2) | Right trapezoid diagonal |
| Area (from diagonals) | A = (d1 x d2 x sin(theta)) / 2 | theta = angle between diagonals |
Frequently Asked Questions
What is the formula for the area of a trapezoid?⌄
Area = (a + b) / 2 x h, where a and b are the parallel sides (bases) and h is the perpendicular height between them. This is equivalent to the average of the two bases times the height.
How do I find the height of a trapezoid?⌄
If you know the area and both bases: h = 2A / (a + b). If you know a leg and the bases: h = sqrt(leg^2 - ((b-a)/2)^2) for an isosceles trapezoid. Our calculator can derive height from leg length.
What is a midsegment (median) of a trapezoid?⌄
The midsegment connects the midpoints of the two non-parallel sides. Its length equals the average of the two bases: m = (a + b) / 2. The midsegment is parallel to both bases.
What is an isosceles trapezoid?⌄
A trapezoid with equal-length non-parallel sides (legs). It has line symmetry, equal base angles, and equal diagonals. Many real-world trapezoids (bridges, building facades) are isosceles.
How do I find the perimeter of a trapezoid?⌄
P = a + b + c + d, where a and b are the parallel sides and c and d are the legs. If only the bases and height are known, you need additional information to find leg lengths.
What is a right trapezoid?⌄
A trapezoid with two right angles (one leg perpendicular to the bases). Common in construction for ramp profiles and roof pitches. One leg equals the height.
How does dilation affect a trapezoid?⌄
A dilation with scale factor k multiplies all side lengths by k, multiplies the area by k^2, and preserves all angles. The resulting trapezoid is similar to the original.
What are real-world examples of trapezoids?⌄
Bucket cross-sections, dam walls, bridge supports, handbag shapes, lamp shades, stadium seating sections, and many architectural elements. The shape distributes weight efficiently.