Isosceles Trapezoid Calculator
Enter the two parallel bases plus either the height or the leg (choose the mode) and get area, height, leg, perimeter, diagonal, and base angles — any consistent unit works.
Example: with Longer base (a) 10 · Shorter base (b) 4 · Third value is the… Height (h) — perpendicular between bases · Height or leg value 4 → Area: 28 square units.
- Height (h)4 units
- Leg (c)5 units each
- Perimeter24 units
Computed by the calculator below using its default values. Change any input to see your own numbers.
Drop two perpendiculars and an isosceles trapezoid becomes a rectangle plus two right triangles — that is the whole method.
Two right triangles do all the work
Drop perpendiculars from the ends of the short base and an isosceles trapezoid splits into a central rectangle plus two identical right triangles. Each triangle's horizontal leg is the overhang (a − b)/2, its vertical leg is the height h, and its hypotenuse is the trapezoid's leg c. That single picture supplies every conversion: c = √(h² + ((a − b)/2)²), and h = √(c² − ((a − b)/2)²) when the leg is what you measured.
Area needs no trigonometry at all — average the two bases and multiply by the height: (a + b)/2 × h. The default 10-and-4 bases with height 4 average to 7, giving 28 square units.
Diagonals and angles
Symmetry makes the two diagonals equal — a property that actually defines the isosceles trapezoid — and each spans √(h² + ((a + b)/2)²). The two angles at the long base match each other, the two at the short base match each other, and each long-short pair sums to 180° because the bases are parallel.
How it’s calculated
With bases a > b: offset = (a − b)/2; leg c = √(h² + offset²), or h = √(c² − offset²) in leg mode; area = (a + b)/2 × h; perimeter = a + b + 2c; diagonal = √(h² + ((a + b)/2)²); base angle = arctan(h/offset). If the entered bases are reversed, the larger is treated as a. Rounded to 3 decimals.
Applies to isosceles trapezoids only — equal legs, equal diagonals, equal base angles; a general trapezoid has two different legs and needs both.
Isosceles trapezoid formulas
| Property | Formula |
|---|---|
| Height from leg | h = √(c² − ((a − b)/2)²) |
| Leg from height | c = √(h² + ((a − b)/2)²) |
| Area | (a + b)/2 × h |
| Diagonal | √(h² + ((a + b)/2)²) |
| Base angle | arctan(h ÷ ((a − b)/2)) |
Derived by dropping perpendiculars from the short base; each end forms a right triangle with legs h and (a − b)/2.
Common mistakes
- Using the slanted leg c as the height h — the height is perpendicular to the bases and always shorter than the leg.
- Taking the full base difference a − b instead of half of it in the right-triangle step.
- Entering a leg shorter than (a − b)/2 in leg mode — the trapezoid cannot close.
- Averaging the bases but forgetting to multiply by the height when computing area.
Frequently asked questions
What is the area formula for an isosceles trapezoid?
Area = (a + b)/2 × h — the average of the two parallel bases times the perpendicular height. It is the same formula as any trapezoid; the isosceles property only helps you find h or the leg.
How do I find the height from the leg?
h = √(c² − ((a − b)/2)²). The leg is the hypotenuse of a right triangle whose horizontal leg is the overhang (a − b)/2, so subtract that overhang squared and take the square root.
What makes a trapezoid isosceles?
The two non-parallel sides (legs) are equal. Equivalent tests: the base angles are equal, or the diagonals are equal — any one of these implies the others.
Why are both diagonals the same length?
Mirror symmetry about the vertical center line maps one diagonal onto the other, so each measures √(h² + ((a + b)/2)²). Unequal diagonals mean the trapezoid is not isosceles.