Right Trapezoid Calculator

Calculate area, perimeter, diagonals, and angles of a right trapezoid with step-by-step solutions.

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Results

Area
--
square units
Perimeter--
Oblique Side (c)--
Diagonal (p) - from right angle corners--
Diagonal (q) - from oblique corners--
Acute Angle at base--
Obtuse Angle at top--

Step-by-Step Solution

What Is a Right Trapezoid?

A right trapezoid (also called a right-angled trapezoid) is a quadrilateral with one pair of parallel sides (bases) and two right angles. The two right angles are adjacent, meaning one of the non-parallel sides (the height) is perpendicular to both parallel sides. The other non-parallel side is called the oblique side or slant side.

Formulas Used

Area

Average of the parallel sides times the height.

A = ((a + b) / 2) x h

Oblique Side

The non-perpendicular leg calculated using Pythagorean theorem.

c = sqrt((b - a)^2 + h^2)

Perimeter

Sum of all four sides.

P = a + b + h + c

Diagonals

The two diagonals of the right trapezoid.

p = sqrt(a^2 + h^2), q = sqrt(b^2 + h^2)

Angles in a Right Trapezoid

A right trapezoid has exactly two right angles (90 degrees each) on the same side. The other two angles are supplementary to each other (they add up to 180 degrees). One of these is acute and the other is obtuse. The acute angle at the base can be found using the arctangent of the height divided by the difference of the bases.

Properties

  • Exactly one pair of parallel sides (bases a and b).
  • Two right angles on one side (the perpendicular side equals the height).
  • The non-right angles are supplementary (sum to 180 degrees).
  • The midsegment (median) has length (a + b) / 2.
  • A right trapezoid can be divided into a rectangle and a right triangle.

Real-World Applications

Right trapezoids appear frequently in architecture (sloped roofs adjoining vertical walls), civil engineering (retaining walls, road embankments), and furniture design. They are also used in calculus as the basis for the trapezoidal rule for numerical integration.