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) × h

a and b are the parallel bases, h is the perpendicular height between them.

Alternative Form

A = ((a + b) / 2) × h

Same formula written as average of bases times height.

Using Median

A = m × h

Where 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.