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
A = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 26.
Example 2
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.