Isosceles Trapezoid Calculator — Area, Perimeter, Diagonal
Enter the two parallel bases and the equal leg length of an isosceles trapezoid to get the area, height, perimeter, diagonal length, and base angles — all in one step.
Area = (a + b) / 2 × h, where h is derived from the leg length
- 1
Leg offset per side
|10 − 6| ÷ 2 = 2Horizontal projection of each equal leg. - 2
Height (Pythagorean theorem)
√(5² − 2²) = √(21) = 4.5826 - 3
Area
(10 + 6) ÷ 2 × 4.5826 = 36.6606
How does this calculator work?
An isosceles trapezoid with parallel bases a, b and equal legs l has height h = √(l²−((a−b)/2)²), area (a+b)/2·h, perimeter a+b+2l, and diagonal √(h²+((a+b)/2)²). All angles and the diagonal follow from these three inputs.
Formula
How this is calculated
An isosceles trapezoid has exactly one pair of parallel sides (the bases a and b) and two equal legs (l). Because the legs are equal, the trapezoid is symmetric about the perpendicular bisector of the bases. The horizontal projection of each leg is x = (a − b)/2, and by the Pythagorean theorem the perpendicular height is h = √(l² − x²). This requires l > x; if the leg is shorter than the offset the trapezoid cannot close and the calculator shows a warning.
The area follows from the standard trapezoid formula A = (a + b)/2 × h. The perimeter is simply a + b + 2l. Each diagonal connects one corner of the long base to the opposite corner of the short base — by coordinate geometry this length is d = √(h² + ((a+b)/2)²). The base angles (at the long base) are equal by symmetry: θ = arctan(h/x). The top angles (at the short base) supplement to 180°.
All properties are determined by a, b, and l. The isosceles trapezoid is the only quadrilateral (other than a rectangle) that is cyclic (inscribed in a circle) among trapezoids; its diagonals are equal in length.
Frequently asked questions
A general (irregular) trapezoid has one pair of parallel sides but unequal legs and asymmetric base angles. An isosceles trapezoid has equal legs, equal base angles, equal diagonals, and is symmetric about the midline — it is the "balanced" trapezoid.
Drop perpendiculars from the top corners to the long base. Each creates a right triangle with hypotenuse l (the leg) and horizontal leg x = (a−b)/2. The Pythagorean theorem gives h = √(l²−x²).
The horizontal offset of each leg is (a−b)/2. The leg must span this offset plus have some height, so l² > x² is required. If l equals x, the height is zero and the shape degenerates to a line segment.
Also known as
TG we-Calculate Editorial Team. (2026). Isosceles Trapezoid Calculator — Area, Perimeter, Diagonal [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/isosceles-trapezoid-calculator
TG we-Calculate Editorial Team. "Isosceles Trapezoid Calculator — Area, Perimeter, Diagonal." TG we-Calculate. 2026. https://we-calculate.com/calculator/isosceles-trapezoid-calculator.
TG we-Calculate Editorial Team, "Isosceles Trapezoid Calculator — Area, Perimeter, Diagonal," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/isosceles-trapezoid-calculator
@misc{wecalculate_isosceles_trapezoid_calculator, title = {Isosceles Trapezoid Calculator — Area, Perimeter, Diagonal}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/isosceles-trapezoid-calculator}}, year = {2026}, note = {TG we-Calculate} }
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