Last updated on August 5th, 2025
A trapezium (or trapezoid in North American terms) is a 2-dimensional shape with four sides, where at least one pair of opposite sides are parallel. The surface area of a trapezium is the total area enclosed within its boundaries. In this article, we will learn about the surface area of a trapezium.
The surface area of a trapezium refers to the total area enclosed by its boundary. It is measured in square units
. A trapezium is a quadrilateral that has two parallel sides known as bases and two non-parallel sides. The bases can be of different lengths, and the distance between them is referred to as the height of the trapezium.
To find the surface area of a trapezium, you need to know the lengths of its two parallel sides (bases) and the height. The formula for the area of a trapezium is:
Area = ½ × (Base₁ + Base₂) × Height
Here, Base₁ and Base₂ are the lengths of the parallel sides, and Height is the perpendicular distance between them.
Let's look at examples to understand how to calculate the surface area of a trapezium.
Calculate the surface area of a trapezium with bases of 8 cm and 12 cm, and a height of 5 cm.
Area = ½ × (8 + 12) × 5 = ½ × 20 × 5 = 10 × 5 = 50 cm²
Find the surface area of a trapezium where the lengths of the bases are 10 m and 15 m, and the height is 7 m.
Area = ½ × (10 + 15) × 7 = ½ × 25 × 7 = 12.5 × 7 = 87.5 m²
A trapezium has bases of 9 in and 14 in, and its height is 6 in.
Calculate the area. Area = ½ × (9 + 14) × 6 = ½ × 23 × 6 = 11.5 × 6 = 69 in²
Students sometimes confuse the lengths of the bases with the height. Remember, the bases are the parallel sides of the trapezium, and the height is the perpendicular distance between them.
Area = ½ × (5 + 7) × 4 = ½ × 12 × 4 = 6 × 4 = 24 cm²
Calculate the area of a trapezium with base lengths of 12 m and 20 m and a height of 8 m.
Area = 128 m²
Area = ½ × (12 + 20) × 8 = ½ × 32 × 8 = 16 × 8 = 128 m²
A trapezium has bases of 6 in and 10 in, and its height is 5 in. Find its surface area.
Area = 40 in²
Area = ½ × (6 + 10) × 5 = ½ × 16 × 5 = 8 × 5 = 40 in²
Find the area of a trapezium with bases 9 cm and 15 cm, and a height of 10 cm.
Area = 120 cm²
Area = ½ × (9 + 15) × 10 = ½ × 24 × 10 = 12 × 10 = 120 cm²
Calculate the surface area of a trapezium with bases of 8 ft and 14 ft, and a height of 9 ft.
Area = 99 ft²
Students often make mistakes while calculating the surface area of a trapezium, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
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