101 LearnersLast updated on August 5th, 2025
Surface Area of Trapezium
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.
What is 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.
Surface Area of a Trapezium Formula
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.
Examples of Calculating Surface Area of a Trapezium
Let's look at examples to understand how to calculate the surface area of a trapezium.
Example 1:
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
Example 2:
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
Example 3:
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
Confusion between Bases and Height
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.
Mistake 1
Incorrectly Adding the Bases
Some students forget to add the lengths of both bases before multiplying by the height. Always ensure you add both Base₁ and Base₂ before proceeding with the calculation.
Mistake 2
Forgetting the ½ Factor in the Formula
A common mistake is forgetting to multiply by ½ in the formula. The area formula for a trapezium includes a ½ factor, crucial for obtaining the correct result.
Mistake 3
Misidentifying the Height
Students sometimes use one of the non-parallel sides as the height. Always use the perpendicular distance between the bases as the height.
Mistake 4
Using Non-Parallel Sides as Bases
Ensure that you are using the parallel sides as the bases in the formula. The non-parallel sides should not be used in place of the bases.
Mistake 5
Solved Examples of Surface Area of Trapezium
Find the surface area of a trapezium with bases of 5 cm and 7 cm, and a height of 4 cm.
Area = 24 cm²
Problem 1
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.
Explanation
Area = 128 m²
Problem 2
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.
Explanation
Area = 40 in²
Problem 3
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.
Explanation
Area = 120 cm²
Problem 4
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.
Explanation
Area = 99 ft²
It is the total area enclosed within the boundaries of the trapezium, calculated using the formula ½ × (Base₁ + Base₂) × Height.
1.What are the bases of a trapezium?
2.How is the height of a trapezium defined?
3.Is the surface area of a trapezium measured in square units?
4.What is the key formula for the surface area of a trapezium?
Common Mistakes and How to Avoid Them in the Surface Area of a Trapezium
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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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
