Summarize this article:
102 LearnersLast updated on September 4, 2025
Surface Area of Trapezoid
A trapezoid is a 2-dimensional shape with two parallel sides. The surface area of a trapezoid is the total area covered by its shape. In this article, we will learn about the surface area of a trapezoid.
What is the Surface Area of a Trapezoid?
The surface area of a trapezoid is the total area occupied by its boundary or surface. It is measured in square units. A trapezoid is a 2D shape with four sides, where one pair of opposite sides is parallel.
The parallel sides are referred to as the bases. The surface area of a trapezoid is determined by the lengths of its bases and its height.
Surface Area of a Trapezoid Formula
A trapezoid's surface area can be calculated using the lengths of its two parallel sides (bases) and its height.
The formula for the surface area of a trapezoid is given as: Surface Area = ½ × (Base1 + Base2) × Height
Base and Height in a Trapezoid
In a trapezoid, the bases are the two parallel sides, and the height is the perpendicular distance between these bases. The formula uses these dimensions to determine the total area occupied by the trapezoid.
Example Calculation of Trapezoid's Surface Area
To calculate the surface area of a trapezoid, you need to know the lengths of the two bases and the height.
For example, consider a trapezoid with base1 = 6 cm, base2 = 10 cm, and height = 4 cm.
Surface Area = ½ × (6 + 10) × 4 = ½ × 16 × 4 = 32 cm²
Common Mistakes in Calculating Surface Area of a Trapezoid
When calculating the surface area of a trapezoid, ensure you identify the correct bases and height. Misidentifying these can lead to incorrect calculations.
Also, remember to use the correct formula: Surface Area = ½ × (Base1 + Base2) × Height
Confusion between Bases and Height
Students may confuse the bases of the trapezoid with its non-parallel sides. Always ensure that the bases are the parallel sides when applying the formula.
Mistake 1
Incorrect Application of the Formula
Some students mistakenly forget to multiply by ½ when using the formula. The correct formula is Surface Area = ½ × (Base1 + Base2) × Height.
Mistake 2
Misidentifying the Height
A common mistake is measuring the slant height instead of the perpendicular height. Always use the perpendicular distance between the bases.
Mistake 3
Forgetting to Sum the Bases
Students sometimes forget to add the lengths of both bases before multiplying by the height. Ensure to add Base1 and Base2 together as part of the formula.
Mistake 4
Using Units Incorrectly
Always ensure that the bases and height are in the same units before calculating the surface area, and express the final area in square units.
Mistake 5
Solved Examples of Surface Area of Trapezoid
Find the surface area of a trapezoid with bases of 8 cm and 12 cm and a height of 5 cm.
Surface Area = 50 cm²
Problem 1
Given Base1 = 8 cm, Base2 = 12 cm, Height = 5 cm. Use the formula: Surface Area = ½ × (Base1 + Base2) × Height = ½ × (8 + 12) × 5 = ½ × 20 × 5 = 50 cm²
A trapezoid has a height of 7 cm, and its bases are 9 cm and 15 cm. Find the surface area.
Explanation
Surface Area = 84 cm²
Problem 2
Use the formula: Surface Area = ½ × (Base1 + Base2) × Height = ½ × (9 + 15) × 7 = ½ × 24 × 7 = 84 cm²
Calculate the surface area of a trapezoid with bases measuring 10 cm and 14 cm, with the height being 6 cm.
Explanation
Surface Area = 72 cm²
Problem 3
Use the formula: Surface Area = ½ × (Base1 + Base2) × Height = ½ × (10 + 14) × 6 = ½ × 24 × 6 = 72 cm²
Find the surface area of a trapezoid with bases of 5 cm and 11 cm and a height of 3 cm.
Explanation
Surface Area = 24 cm²
Problem 4
Use the formula: Surface Area = ½ × (Base1 + Base2) × Height = ½ × (5 + 11) × 3 = ½ × 16 × 3 = 24 cm²
A trapezoid has bases of 7 cm and 13 cm, and a height of 4 cm. What is its surface area?
Explanation
Surface Area = 40 cm²
It is the total area covered by the trapezoid, calculated using its two parallel sides (bases) and height.
1.What formula is used for finding the surface area of a trapezoid?
2.What is the significance of the height in a trapezoid?
3.How do you identify the bases in a trapezoid?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Trapezoid
Students often make mistakes while calculating the surface area of a trapezoid, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
Explore More measurement
![Important Math Links Icon]()
Previous to Surface Area of Trapezoid
![Important Math Links Icon]()
Next to Surface Area of Trapezoid
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
