Area of a Trapezoid
Area of a trapezoid with parallel sides a and b.
Formula
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Example
Parallel sides 6 and 10, height 4: A = ½(6+10)·4 = 32.
How it works
A trapezoid is a four-sided shape with one pair of parallel sides, and the area formula uses the average of those two parallel sides multiplied by the perpendicular height. This works because you can think of the trapezoid as being equivalent to a rectangle whose width is the average length of the two bases and whose height is the distance between them. So the formula finds the same area you would get by "smoothing out" the slanted sides into an equivalent rectangle.
When to use it
Use this formula whenever you need the area of a trapezoid in geometry, measurement, or design problems. It also appears in real-world settings like land surveying, architecture, and engineering when a region or face has a trapezoid shape.
Worked example, step by step
Let the parallel sides be a = 8 cm and b = 14 cm, and the height be h = 5 cm. A = 1/2(a + b)h A = 1/2(8 + 14)(5) A = 1/2(22)(5) A = 11 × 5 A = 55 cm²
Common mistakes to avoid
- Using the slanted side instead of the perpendicular height
- Forgetting to add the two parallel sides before multiplying by 1/2
- Giving the answer in linear units instead of square units
Did You Know?
The trapezoid rule for area is also the basis of numerical integration in engineering.
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