Surface Area of Trapezium
2026-02-28 08:50 Diff
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Last updated on August 5, 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.

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.

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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.

Problem 1

Area = ½ × (5 + 7) × 4 = ½ × 12 × 4 = 6 × 4 = 24 cm²

Okay, lets begin

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

Well explained 👍

Problem 2

Area = ½ × (12 + 20) × 8 = ½ × 32 × 8 = 16 × 8 = 128 m²

Okay, lets begin

A trapezium has bases of 6 in and 10 in, and its height is 5 in. Find its surface area.

Explanation

Area = 40 in²

Well explained 👍

Problem 3

Area = ½ × (6 + 10) × 5 = ½ × 16 × 5 = 8 × 5 = 40 in²

Okay, lets begin

Find the area of a trapezium with bases 9 cm and 15 cm, and a height of 10 cm.

Explanation

Area = 120 cm²

Well explained 👍

Problem 4

Area = ½ × (9 + 15) × 10 = ½ × 24 × 10 = 12 × 10 = 120 cm²

Okay, lets begin

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

Well explained 👍

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?

The bases of a trapezium are the two parallel sides.

2.How is the height of a trapezium defined?

The height is the perpendicular distance between the two parallel bases.

3.Is the surface area of a trapezium measured in square units?

Yes, the surface area is measured in square units like cm², m², or in².

4.What is the key formula for the surface area of a trapezium?

The key formula is Area = ½ × (Base₁ + Base₂) × Height.

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