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Right Trapezoid Calculator | Solve Geometry From Bases and Height

Quick reference

Bases a, b	Height h	Area	Slant side
10, 6	3	24	5
12, 8	5	50	6.40
20, 14	8	136	10
9, 9	4	36	4 (rectangle)

info Right Trapezoid Calculator

Free math calculator — enter your numbers and get an instant, accurate result.

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info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

Property	What it tells you
Two right angles	Both sit on the perpendicular leg (the height)
Slant side	Hypotenuse of the right triangle with legs h and (a − b)
Acute angle	Always at the long base, next to the slant side
a = b	The shape degenerates into a rectangle (slant = h)

lightbulb A retaining-wall cross-section: bases 14 and 8, height 5

A concrete retaining wall has a trapezoidal cross-section: the long base is 14 ft, the short base 8 ft, and the height 5 ft. Find the area (concrete per foot of wall), the slant face, the perimeter, and the angles.

Result: Area = (14 + 8) ÷ 2 × 5 = 55 ft². Slant = √((14−8)² + 5²) = √61 ≈ 7.810 ft. Perimeter = 14 + 8 + 5 + 7.810 ≈ 34.810 ft. Diagonals: √(14²+5²) ≈ 14.867 ft and √(8²+5²) ≈ 9.433 ft. Angles: arctan(5/6) ≈ 39.8° at the long base, 140.2° opposite, plus the two 90° corners.

What this means: The 55 ft² area tells the concrete order — 55 cubic feet per linear foot of wall. The 7.81 ft slant is the formwork length for the sloped face, and the 39.8°/140.2° angles set the batter of the wall. Every figure comes from the same three inputs, fully determined.

Formula & methodology

Formula: Area = (a + b) ÷ 2 × h; slant c = √((a − b)² + h²); perimeter = a + b + h + c

How a right trapezoid is solved

A right trapezoid has two parallel bases (a, b) and two right angles, making the height h also the perpendicular leg. Everything follows from three inputs:

Area: (a + b) ÷ 2 × h — the average base times height.
Slant side: √((a − b)² + h²) — the hypotenuse of the right triangle formed by the height and the base difference.
Perimeter: a + b + h + slant.
Diagonals: √(a² + h²) and √(b² + h²).
Angles: two are 90°; the acute angle is arctan(h ÷ (a − b)), the obtuse one its supplement.

Example: a = 14, b = 8, h = 5 → area 55, slant √61 ≈ 7.81, perimeter ≈ 34.81, angles 90°, 90°, ≈ 39.8°, ≈ 140.2°.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What is a right trapezoid?

The Right Trapezoid Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Calculates the area, slant side, perimeter, diagonals and angles of a right trapezoid from its two parallel bases and height. There is no limit on usage, and it works on any device.

How do you find the area of a right trapezoid?

Enter the required values into the input fields and press the calculate button. The tool applies the formula Area = (a + b) ÷ 2 × h; slant c = √((a − b)² + h²); perimeter = a + b + h + c and returns the result with a short explanation of each step, so you can check the working yourself.

How do you find the slant side of a right trapezoid?

Use the Pythagorean theorem with the height and the base difference: slant = √(height² + (base₁ − base₂)²). For a trapezoid with bases 10 and 6 and height 8, the slant is √(64 + 16) = √80 ≈ 8.94. The calculator derives it from the two bases and the height, then uses it for the perimeter.

Can a right trapezoid have equal bases?

If the bases are equal, the shape is a rectangle — a trapezoid with one pair of parallel sides degenerates into a parallelogram (rectangle when right) when the parallel sides match. The calculator handles this gracefully: the slant side becomes the height, and the formulas still work. The area formula (base₁ + base₂) ÷ 2 × height reduces to base × height.

What are the angles of a right trapezoid?

A right trapezoid has two 90° angles by definition — the right angles at the legs that are perpendicular to the bases. The other two angles are supplementary and depend on the base lengths: with bases 10 and 6 and height 8, one acute angle is about 63.4° and the other obtuse is 116.6°. The calculator returns all four angles.

How do I find the angles of a trapezoid?

Co-interior angles between the parallel sides always sum to 180°. A right trapezoid fixes two of them at 90°, so only one angle needs computing: with parallel sides 10 and 6 and height 5, the slant leg rises over a run of 4, making the acute angle tan⁻¹(5/4) = 51.3° and its partner 128.7°. All four angles of any trapezoid total 360°.

How do you find the slant side by hand?

Treat the height and the base difference as the legs of a right triangle: slant = √(h² + (a−b)²). For bases 14 and 8 with height 5, that's √(25 + 36) = √61 ≈ 7.81. The page shows this Pythagorean step explicitly so the number is never mysterious.

How are the diagonals calculated?

Each diagonal is a hypotenuse: the long-base diagonal is √(a² + h²) and the short-base diagonal is √(b² + h²). For 14, 8, 5 that gives ≈ 14.87 ft and ≈ 9.43 ft. They're useful for checking squareness when laying out the shape full-size.

What are the four interior angles?

Two are 90° by definition — that's what makes it a right trapezoid. The acute angle sits at the long base next to the slant side: arctan(h/(a−b)) ≈ 39.8° here. The fourth angle is its supplement, 180° − 39.8° = 140.2°, since consecutive angles between the parallel sides always sum to 180°.

What happens if the two bases are equal?

The shape becomes a rectangle: the slant side equals the height, the area is simply base × height, and all angles are 90°. The formulas handle it naturally — with a = b the base difference is zero, so slant = √(h²) = h. Nothing breaks; the trapezoid just degenerates gracefully.

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