How this instrument works
A right trapezoid has exactly one pair of parallel sides — the two bases — and exactly one pair of right angles, both sitting where a single leg meets the bases at 90°. That leg is the height, running straight up from the longer base to the shorter one. The fourth side, called the slant leg, leans instead of standing straight, closing the gap between the two base lengths at whatever angle the geometry demands.
That single perpendicular leg is what makes the shape solvable from so little information. Drop a vertical line from the top of the short base down to the long base and a small right triangle appears, with legs h and (b2 − b1) — the height and the horizontal overhang left once the shorter base is subtracted from the longer. The slant leg is that triangle's hypotenuse, so the Pythagorean theorem hands it over directly: slant = √(h² + (b2 − b1)²). A general trapezoid offers no such shortcut — without a right angle to anchor a triangle inside it, the fourth side has to be measured, not derived from the other three.
The formula degrades gracefully at its limits. Let the two bases become equal and the horizontal overhang (b2 − b1) vanishes, so slant collapses to exactly h — the shape has quietly become a rectangle, still technically a trapezoid under the inclusive definition, now with two pairs of right angles instead of one. Push b1 toward zero instead and the short base disappears, leaving a plain right triangle with legs b2 and h.
- Enter the shorter parallel side into Base 1 (shorter) and the longer one into Base 2 (longer).
- Enter the perpendicular leg's length into Height (the perpendicular leg) — the side that meets both bases at a right angle.
- Read Slant leg length for the fourth side, recovered by the Pythagorean theorem from the height and the difference between the two bases.
- Read Area and Perimeter for the enclosed area and the total distance around all four sides.
Worked example — a 6-10-4 ramp side panel
A loading ramp's side panel is a right trapezoid: the vertical back rises Height h = 4 ft from the ground to the platform, the platform forms Base 1 = 6 ft, and the ground runs out to Base 2 = 10 ft before the sloped face lands. The slant leg is slant = √(4² + (10 − 6)²) = √(16 + 16) = √32 ≈ 5.656854 ft, the exact board length to cut for the sloped face — and the area is A = ½(6 + 10) × 4 = ½ × 16 × 4 = 32 ft², the plywood needed to skin one side.
Perimeter adds all four edges: P = 6 + 10 + 4 + 5.656854 ≈ 25.657 ft, the total trim length for framing the panel's outline. Notice the slant leg's underlying right triangle has legs of 4 ft and 4 ft, an isosceles right triangle, so the sloped face leans at a clean 45° even though its own length, √32, is not a whole number.
Questions
What makes a trapezoid a right trapezoid?
It has exactly one pair of right angles, both formed where a single leg meets the two parallel bases at 90°. That perpendicular leg doubles as the height; the opposite leg slants and is not perpendicular to either base. A general trapezoid has no right angles at all, and an isosceles trapezoid has none either, relying instead on mirror symmetry between its two slanted legs.
How is the slant leg calculated without measuring it directly?
The height and the two bases fix it. Drop a vertical from the short base down to the long one and a right triangle appears with legs h and (b2 − b1); the slant leg is its hypotenuse, so slant = √(h² + (b2 − b1)²) by the Pythagorean theorem. For bases 6 and 10 with height 4, that is √(4² + 4²) = √32 ≈ 5.657.
Why does this calculator need only three measurements?
Because the right angle removes a degree of freedom that a general trapezoid keeps free. In an ordinary trapezoid the two legs can lean at any independent angles, so a fourth measurement is required before area and perimeter can both be pinned down. Here, one leg is already fixed perpendicular to the bases, so the Pythagorean theorem supplies the other leg for free from what you already entered.
Does the right angle change the area formula too?
No — area still comes from A = ½(b1 + b2)h, exactly the formula used for any trapezoid, right-angled or not, because that identity only ever needed the bases and the perpendicular height. What the right angle changes is the perimeter: a general trapezoid needs its leg lengths measured directly, while a right trapezoid's slant leg falls out of the Pythagorean theorem instead.
What happens if both bases are equal in length?
The trapezoid degenerates into a rectangle. With b1 = b2, the horizontal offset (b2 − b1) is zero, so slant = √(h² + 0²) = h — the fourth side becomes perpendicular too, and all four angles turn into right angles instead of just one pair.
Is the height the same as one of the trapezoid's legs here?
Yes, and that is specific to right trapezoids. In a general trapezoid, height is a perpendicular measurement taken between the bases, independent of either leg's actual length. In a right trapezoid, one leg happens to run exactly along that perpendicular path, so its length and the height are the same number, entered once into the Height field.