Right Trapezoid Area Calculator

Calculate the area of a right trapezoid from dimensions or coordinates with step-by-step solutions.

Choose Method

Results

Area
--
square units

Step-by-Step Solution

Right Trapezoid Area Formula

The area of a right trapezoid is calculated using the same formula as any trapezoid: the average of the two parallel sides (bases) multiplied by the perpendicular height between them. In a right trapezoid, one of the non-parallel sides IS the height, since it is perpendicular to both bases.

Methods for Calculating Area

From Side Lengths

Using the two parallel sides and the height (perpendicular side).

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

From Coordinates

Using the Shoelace formula with four vertices.

A = |sum(x_i*y_{i+1} - x_{i+1}*y_i)| / 2

Decomposition Method

Split into a rectangle (area = a x h) and a right triangle (area = (b-a) x h / 2).

A = a*h + (b-a)*h/2

Understanding the Formula

The formula A = ((a + b) / 2) x h can be understood intuitively: (a + b) / 2 gives the average length of the two parallel sides (the midsegment), and multiplying by h gives the area. This is equivalent to "stretching" the trapezoid into a rectangle with width equal to the midsegment.

Why Use Coordinates?

The coordinate method (Shoelace formula) is useful when you know the exact positions of the vertices but not necessarily the side lengths. It works for any polygon and automatically handles the area calculation without needing to identify which sides are parallel or perpendicular. This method is commonly used in surveying, computer graphics, and GIS applications.

Quick Tips

  • The height must be perpendicular to the two parallel sides.
  • In a right trapezoid, the height equals the length of the perpendicular side.
  • The formula simplifies to a rectangle formula when a = b.
  • The formula simplifies to a triangle formula when one base is 0.
  • Always double-check that all measurements use the same units.