How to Calculate the Area of a Trapezoid
A trapezoid (or trapezium in British, Australian, and Indian English) is a 2D quadrilateral with at least one pair of parallel opposite sides, known as bases. The perpendicular distance between these parallel bases is the height ($h$).
The Standard Area Formula
Area = ½ × (a + b) × h = ((a + b) × h) / 2
Where:
- a = Length of first parallel base
- b = Length of second parallel base
- h = Perpendicular height between base a and base b
Step-by-Step Example Calculation
Suppose you have a trapezoid with top base a = 8 cm, bottom base b = 14 cm, and perpendicular height h = 5 cm:
- Sum the parallel bases: 8 + 14 = 22 cm
- Take the average: 22 ÷ 2 = 11 cm
- Multiply by the perpendicular height: 11 × 5 = 55 cm²
The total surface area is 55 square centimeters (cm²).