dopecalc

Trapezoid Calculator

Calculate the area and perimeter of a trapezoid. Compute area using bases and height, or find perimeter from all four sides.

About this Calculator

Calculate the area and perimeter of a trapezoid. Compute area using bases and height, or find perimeter from all four sides.

Formula & Calculations

Formula

Area = ½(a + b)h; Perimeter = a + b + c + d (when all four sides are known)
Where:
  • a, b=The two parallel bases of the trapezoid
  • h=Height (perpendicular distance between the parallel bases)
  • c, d=The non-parallel legs of the trapezoid (used for perimeter only)
  • A=Area of the trapezoid
  • P=Perimeter of the trapezoid

Assumptions

  • Bases a and b are parallel. Height h is perpendicular to both bases.
  • For perimeter calculation, all four sides (a, b, c, d) must be provided.
  • Area calculation requires both bases and the height.
  • All measurements use consistent units.

Calculation Examples

Example 1

Inputs:Base a = 8, Base b = 5, Height h = 4
Result:Area = 26 square units

A = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 26.

Example 2

Inputs:a = 10, b = 6, c = 5, d = 7
Result:Perimeter = 28 units

P = 10 + 6 + 5 + 7 = 28.

Frequently Asked Questions

What is a trapezoid?

A trapezoid (also called a trapezium in some countries) is a quadrilateral with at least one pair of parallel sides. These parallel sides are called bases. A trapezoid with two pairs of parallel sides is a parallelogram.

Why is the area formula ½(a + b)h?

The formula averages the two bases and multiplies by the height. Visually, this can be understood by duplicating the trapezoid, rotating one copy, and joining them to form a parallelogram with base (a + b) and height h. The area of the parallelogram is (a + b)h, so the trapezoid's area is half of that.