Isosceles Trapezoid Area Calculator
Enter the two parallel bases and the equal leg of an isosceles trapezoid to instantly get the area, height, perimeter, diagonal length, and interior angles.
Area = ½ × (a + b) × h
- 1
Horizontal offset per side
(10 − 6) ÷ 2 = 2Each leg sits this far in from the end of the longer base. - 2
Height² (Pythagorean theorem)
5² − 2² = 21 - 3
Height
√(21) = 4.5826 - 4
Area
½ × (10 + 6) × 4.5826 = 36.6606
How does this calculator work?
For an isosceles trapezoid with parallel bases a and b (a > b) and equal leg c, compute h = √(c² − ((a−b)/2)²), then Area = ½(a+b)h. The diagonal is √(ab + c²), base angle = arcsin(h/c), and perimeter = a + b + 2c.
Formula
How this is calculated
An isosceles trapezoid has two parallel sides (the longer base a and the shorter base b) and two equal non-parallel legs of length c. Because the shape is symmetric, each leg sits on a horizontal offset of (a − b) / 2 from the end of the longer base. The height h is found by applying the Pythagorean theorem to that right triangle: h = √(c² − ((a − b) / 2)²).
Once the height is known, the area follows the standard trapezoid formula: Area = ½ × (a + b) × h — the average of the two parallel sides times the perpendicular distance between them. The perimeter is simply a + b + 2c. Each diagonal of an isosceles trapezoid has the same length, derived from coordinates as d = √(ab + c²).
The base angle (the acute angle at each end of the longer base) is arcsin(h / c). The top angle (at each end of the shorter base) is the supplement 180° − base angle. If the leg c is too short to span the height — meaning c < (a − b) / 2 — no valid trapezoid exists and the result is hidden.
Frequently asked questions
A trapezoid is isosceles when its two non-parallel sides (legs) are equal in length. This symmetry also forces the two base angles to be equal and the two diagonals to be equal.
Drop a perpendicular from each end of the shorter base to the longer base. This creates a right triangle with hypotenuse c (the leg) and base (a − b) / 2. The height is h = √(c² − ((a − b) / 2)²).
By definition a trapezoid has two parallel sides of different lengths. If they were equal the shape would be a parallelogram (or rectangle), not a trapezoid. The calculator requires a > b to enforce this.
TG we-Calculate Editorial Team. (2026). Isosceles Trapezoid Area Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/isosceles-trapezoid-area-calculator
TG we-Calculate Editorial Team. "Isosceles Trapezoid Area Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/isosceles-trapezoid-area-calculator.
TG we-Calculate Editorial Team, "Isosceles Trapezoid Area Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/isosceles-trapezoid-area-calculator
@misc{wecalculate_isosceles_trapezoid_area_calculator, title = {Isosceles Trapezoid Area Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/isosceles-trapezoid-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
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