Area of a Trapezoid
Calculate the area of a trapezoid using A = ½(a + b)h.
Find the area from two parallel sides and the height with examples.
The Formula
A = ½ × (a + b) × h
This formula calculates the area of a trapezoid (also called a trapezium in some countries).
A trapezoid has exactly one pair of parallel sides.
Variables
| Symbol | Meaning |
|---|---|
| A | Area of the trapezoid |
| a | Length of one parallel side (base 1) |
| b | Length of the other parallel side (base 2) |
| h | Perpendicular height between the two parallel sides |
Example 1
Find the area of a trapezoid with parallel sides of 8 cm and 12 cm, and height 5 cm
a = 8, b = 12, h = 5
A = ½ × (8 + 12) × 5
A = ½ × 20 × 5 = ½ × 100
A = 50 cm²
Example 2
A garden bed is shaped like a trapezoid with parallel sides of 3 m and 5 m, and a height of 2.4 m
a = 3, b = 5, h = 2.4
A = ½ × (3 + 5) × 2.4
A = ½ × 8 × 2.4 = ½ × 19.2
A = 9.6 m²
When to Use It
Use the area of a trapezoid formula when:
- Calculating the area of shapes with two parallel sides of different lengths
- Working with cross-sections of channels, ditches, or embankments
- Measuring irregularly shaped land plots that have two parallel edges
- Solving geometry problems involving trapezoids