For a trapezoid with parallel sides of lengths a and b and perpendicular height h, the area is A = ½(a + b)h. In common UK school terminology, this shape is called a trapezium. Terminology varies, so check the definition used by your course.
Identify the two parallel sides
The formula averages the lengths of the parallel sides and multiplies by the height. Do not select two adjacent sides simply because their measurements are shown. Mark the parallel pair first and confirm that both lengths use the same units.
Use perpendicular height
Height is the shortest distance between the parallel sides, measured at a right angle. A sloping side is not generally the height. If only a sloping length is supplied, you may need additional information or geometry to obtain h.
Calculate the area step by step
Add the two parallel lengths, divide by two and multiply by the perpendicular height. For parallel sides 6 cm and 10 cm with height 4 cm, the calculation is ½ × (6 + 10) × 4 = 32 cm². The squared unit matters because area measures a two-dimensional region.
Area is different from perimeter
Perimeter adds all boundary lengths. Knowing the area does not automatically give the perimeter, because sloping side lengths may still be unknown. Check which quantity the question requests before choosing a formula.
What about surface area?
A trapezoid is two-dimensional, so “area” is the appropriate quantity. If the question describes a solid with trapezoidal faces, its total surface area requires the area of every exposed face. The single trapezoid formula does not provide that total.
Related study guides
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