How to Use This Calculator
- Enter the length of the first parallel base (Base 1)
- Enter the length of the second parallel base (Base 2)
- Enter the perpendicular height between the two bases
- Click "Calculate Area" to get the result
Trapezoid Area Formula
The area of a trapezoid is calculated using the formula:
Area = ½ × (Base 1 + Base 2) × Height
Or expressed mathematically: A = ½ × (a + b) × h
Where:
- a = length of the first parallel base
- b = length of the second parallel base
- h = perpendicular height between the bases
What is a Trapezoid?
A trapezoid (or trapezium in British English) is a quadrilateral with at least one pair of parallel sides. The
parallel sides are called bases, and the perpendicular distance between them is the height. Trapezoids
are commonly found in architecture, engineering, and everyday objects.
Examples
Example 1: Base 1 = 4 units, Base 2 = 6 units, Height = 5 units
Area = ½ × (4 + 6) × 5 = ½ × 10 × 5 = 25 square units
Example 2: Base 1 = 10 cm, Base 2 = 6 cm, Height = 7 cm
Area = ½ × (10 + 6) × 7 = ½ × 16 × 7 = 56 cm²
Example 3: Base 1 = 12 m, Base 2 = 12 m, Height = 8 m
Area = ½ × (12 + 12) × 8 = ½ × 24 × 8 = 96 m²
(This is actually a parallelogram since both bases are equal!)
Common Applications
- Architecture and construction: Roof designs, building structures
- Land surveying and property measurement: Calculating lot areas
- Engineering: Bridge supports, structural components
- Educational mathematics and geometry problems
- Graphic design and digital art: Creating shapes and layouts
Important Notes
- All measurements must be in the same unit for accurate results
- The height must be perpendicular to both bases
- If both bases are equal, the trapezoid is actually a parallelogram
- The bases must be parallel to each other
- All values must be positive numbers