Right Trapezoid — Definition, Formula & Examples

A right trapezoid is a trapezoid that has two adjacent right angles (90°). One of its legs is perpendicular to both bases, which means that leg also serves as the height of the trapezoid.

A right trapezoid is a quadrilateral with exactly one pair of parallel sides (called bases) and two consecutive interior angles each measuring 90°. The leg joining the right angles is perpendicular to both bases and equals the altitude of the trapezoid.

Key Formula

A = \frac{1}{2}(b_1 + b_2) \cdot h

Where:

$b_1$ = Length of the shorter base
$b_2$ = Length of the longer base
$h$ = Height (the leg perpendicular to both bases)

Worked Example

Problem: A right trapezoid has bases of 6 cm and 10 cm. The perpendicular leg (height) is 4 cm. Find its area.

Add the bases: Sum the two parallel sides.

b_1 + b_2 = 6 + 10 = 16 \text{ cm}

Apply the area formula: Multiply the sum of the bases by the height, then divide by 2.

A = \frac{1}{2}(16)(4) = 32 \text{ cm}^2

Answer: The area of the right trapezoid is 32 cm².

Why It Matters

Right trapezoids appear frequently in architecture and cross-sections of ramps or stairs because one side stands straight up. Recognizing that the perpendicular leg equals the height simplifies area and perimeter calculations compared to other trapezoids where you must compute the altitude separately.

Common Mistakes

Mistake: Using the slanted (non-perpendicular) leg as the height in the area formula.

Correction: Only the leg that forms the two 90° angles is the height. The slanted leg is longer than the height unless the trapezoid happens to be a rectangle.