Trapezoid Area Calculator
Calculate the area of a trapezoid (trapezium) instantly. Enter the two parallel bases and perpendicular height.
What is the Area of a Trapezoid?
A trapezoid (called trapezium in British English) is a quadrilateral with exactly one pair of parallel sides called bases. The area is calculated as half the sum of the parallel bases times the height: A = ½(a + b)h. This formula essentially finds the average of the two bases and multiplies by the height.
Trapezoid Area
A = ½(a + b) × ha and b are the parallel bases, h is the perpendicular height between them.
Alternative Form
A = ((a + b) / 2) × hSame formula written as average of bases times height.
Using Median
A = m × hWhere m = (a + b)/2 is the median (midsegment) of the trapezoid.
Examples
Basic: bases 4 and 8, height 5
A = ½(4 + 8) × 5 = ½ × 12 × 5 = 30 = 30
Swimming Pool: bases 10m and 15m, height 8m
A = ½(10 + 15) × 8 = ½ × 25 × 8 = 100 m² = 100 m²
Road Section: bases 20ft and 30ft, height 50ft
A = ½(20 + 30) × 50 = ½ × 50 × 50 = 1250 ft² = 1250 ft²
Isosceles Trapezoid: bases 6 and 10, legs 5 each
Height = √(5² - 2²) = √21 ≈ 4.58. A = ½(6+10) × 4.58 ≈ 36.7 = ≈ 36.7
Frequently Asked Questions
What is the formula for the area of a trapezoid?
The area of a trapezoid is A = ½(a + b) × h, where a and b are the two parallel bases and h is the perpendicular height between them.
Why do we add the bases together?
Adding the bases and dividing by 2 gives the average base length. Multiplying this average by the height gives the area—as if the trapezoid were a rectangle with that average width.
What is the difference between a trapezoid and a trapezium?
In American English, 'trapezoid' means a quadrilateral with one pair of parallel sides. In British English, 'trapezium' means the same thing. The meanings are swapped in some older texts.
How do I find the height of a trapezoid?
If you know the area and both bases: h = 2A / (a + b). For an isosceles trapezoid with known leg length, use the Pythagorean theorem with the horizontal difference of the bases.
Is a parallelogram a trapezoid?
Technically yes, by the inclusive definition (at least one pair of parallel sides). But by the exclusive definition (exactly one pair), a parallelogram is not a trapezoid since it has two pairs of parallel sides.