Trapezoid Area Calculator: formula and examples

A trapezoid is a quadrilateral with at least one pair of parallel sides called bases. This calculator lets you compute the area of any trapezoid from the lengths of its two bases and its height.

Trapezoid area formula

The area is the average of the bases multiplied by the height:

A = 0.5 × (a + b) × h

Where a and b are the lengths of the parallel bases and h is the perpendicular height between them. This formula works for isosceles, scalene and right trapezoids alike.

Example 1: trapezoid with integer bases

Problem: A trapezoid has base a = 10 cm, base b = 6 cm and height h = 4 cm.

1. Sum of bases:
   • a + b = 10 + 6 = 16 cm.
2. Area:
   • A = 0.5 × 16 × 4 = 32 cm².

Answer: A = 32 cm².

Example 2: trapezoid with decimal measurements

Problem: A trapezoid has base a = 7.5 m, base b = 4.2 m and height h = 3.8 m.

1. Sum of bases:
   • a + b = 7.5 + 4.2 = 11.7 m.
2. Area:
   • A = 0.5 × 11.7 × 3.8 ≈ 22.23 m².

Answer: A ≈ 22.23 m².

Usi comuni

• Computing areas of trapezoidal land plots in surveying and topography.
• Determining surface areas of ramps, sloped roofs or cross-sections.
• Solving geometry problems in secondary school mathematics.
• Estimating material quantities for trapezoidal surface coverings.
• Calculating cross-sectional areas in civil engineering, such as channels or dams.
• Designing graphic elements and layouts with trapezoidal proportions.

Common mistakes when calculating trapezoid areas

• Using the non-parallel sides instead of the bases in the formula.
• Confusing the perpendicular height with the length of the slanted sides.
• Forgetting to divide by 2 (or multiply by 0.5) when applying the formula.
• Mixing units, such as bases in cm and height in meters.

Consiglio professionale

If you do not know the height directly but have the slanted side lengths and bases, you can compute the height using the Pythagorean theorem on the right triangle formed by the height, the base difference and the slanted side.