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102 LearnersLast updated on September 4, 2025
Surface Area of Trapezoidal Prism
A trapezoidal prism is a three-dimensional shape that has two parallel trapezoidal bases. The surface area of the trapezoidal prism is the total area covered by its outer surface. The surface area includes the areas of the two trapezoidal bases and the lateral surfaces connecting them. In this article, we will learn about the surface area of a trapezoidal prism.
What is the Surface Area of a Trapezoidal Prism?
The surface area of a trapezoidal prism is the total area occupied by the boundary or surface of the prism. It is measured in square units.
A trapezoidal prism is a 3D shape with two parallel trapezoidal bases and rectangular lateral sides connecting the corresponding sides of the trapezoids.
The surface area of a trapezoidal prism includes the area of its bases and its lateral surfaces.
Surface Area of a Trapezoidal Prism Formula
A trapezoidal prism has two types of surfaces: the trapezoidal bases and the lateral surfaces. The surface area of a trapezoidal prism is given by the formula:
Surface Area = 2 × Area of Base + Lateral Surface Area
The area of the trapezoidal base is calculated as: Area of Base = ½ × (Base1 + Base2) × Height of Trapezoid
The lateral surface area is the sum of the areas of the rectangular sides connecting the trapezoidal bases.
Area of the Trapezoidal Base
The area of the trapezoidal base of the prism is calculated using the formula:
Area of Base = ½ × (Base1 + Base2) × Height of Trapezoid
Here, Base1 and Base2 are the lengths of the parallel sides of the trapezoid, and the Height is the perpendicular distance between these two sides.
Lateral Surface Area of a Trapezoidal Prism
The lateral surface area is the total area of the rectangular sides connecting the trapezoidal bases.
The lateral surface area can be calculated by finding the area of each rectangle and summing them. Each rectangle is formed by the height of the prism and the side of the trapezoid.
Volume of a Trapezoidal Prism
The volume of a trapezoidal prism measures how much space is inside it. It is calculated by multiplying the area of the base by the height (length) of the prism:
Volume = Area of Base × Height of Prism
Confusion between Base Area and Lateral Surface Area
Students sometimes confuse the area of the trapezoidal base with the lateral surface area. Remember that the base area is specific to the trapezoidal shape, while the lateral surface area covers the rectangular sides.
Mistake 1
Using Incorrect Height for Base Area
Some students mistakenly use the height of the prism instead of the height of the trapezoid when calculating the base area. Ensure you use the correct height for the trapezoidal base.
Mistake 2
Neglecting to Sum All Lateral Surfaces
A common mistake is to calculate only one side of the lateral surface area. Make sure to include all rectangular sides when calculating the total lateral surface area.
Mistake 3
Assuming Bases Are Always Identical
Students may assume that both bases are identical, which is not always the case in irregular trapezoidal prisms. Always check the dimensions of each base.
Mistake 4
Misapplying the Volume Formula
Some students confuse the formula for volume with that for surface area. Ensure that for volume, you multiply the area of the base by the height of the prism.
Mistake 5
Solved Examples of Surface Area of Trapezoidal Prism
Find the surface area of a trapezoidal prism with base1 = 6 cm, base2 = 4 cm, height of trapezoid = 5 cm, and height of prism = 10 cm. Assume all lateral sides are equal.
Surface Area = 220 cm²
Problem 1
Area of Base = ½ × (Base1 + Base2) × Height of Trapezoid = ½ × (6 + 4) × 5 = ½ × 10 × 5 = 25 cm² Lateral Surface Area = Perimeter of Base × Height of Prism Perimeter of Base = Base1 + Base2 + 2 × Height of Trapezoid = 6 + 4 + 2 × 5 = 20 cm Lateral Surface Area = 20 × 10 = 200 cm² Total Surface Area = 2 × Area of Base + Lateral Surface Area = 2 × 25 + 200 = 50 + 200 = 250 cm²
Find the surface area of a trapezoidal prism with base1 = 8 cm, base2 = 5 cm, height of trapezoid = 4 cm, and height of prism = 12 cm.
Explanation
Surface Area = 376 cm²
Problem 2
Area of Base = ½ × (Base1 + Base2) × Height of Trapezoid = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 26 cm² Lateral Surface Area = Perimeter of Base × Height of Prism Perimeter of Base = Base1 + Base2 + 2 × Height of Trapezoid = 8 + 5 + 2 × 4 = 21 cm Lateral Surface Area = 21 × 12 = 252 cm² Total Surface Area = 2 × Area of Base + Lateral Surface Area = 2 × 26 + 252 = 52 + 252 = 304 cm²
A trapezoidal prism has base1 = 10 cm, base2 = 7 cm, height of trapezoid = 6 cm, and height of prism = 15 cm. Find the surface area.
Explanation
Surface Area = 620 cm²
Problem 3
Area of Base = ½ × (Base1 + Base2) × Height of Trapezoid = ½ × (10 + 7) × 6 = ½ × 17 × 6 = 51 cm² Lateral Surface Area = Perimeter of Base × Height of Prism Perimeter of Base = Base1 + Base2 + 2 × Height of Trapezoid = 10 + 7 + 2 × 6 = 29 cm Lateral Surface Area = 29 × 15 = 435 cm² Total Surface Area = 2 × Area of Base + Lateral Surface Area = 2 × 51 + 435 = 102 + 435 = 537 cm²
Find the surface area of a trapezoidal prism with base1 = 5 cm, base2 = 3 cm, height of trapezoid = 4 cm, and height of prism = 7 cm.
Explanation
Surface Area = 182 cm²
Problem 4
Area of Base = ½ × (Base1 + Base2) × Height of Trapezoid = ½ × (5 + 3) × 4 = ½ × 8 × 4 = 16 cm² Lateral Surface Area = Perimeter of Base × Height of Prism Perimeter of Base = Base1 + Base2 + 2 × Height of Trapezoid = 5 + 3 + 2 × 4 = 16 cm Lateral Surface Area = 16 × 7 = 112 cm² Total Surface Area = 2 × Area of Base + Lateral Surface Area = 2 × 16 + 112 = 32 + 112 = 144 cm²
The lateral surface area of a trapezoidal prism is 240 cm², and the height of the prism is 10 cm. Find the perimeter of the base.
Explanation
Perimeter of Base = 24 cm
It is the total area that covers the outside of the trapezoidal prism, including its trapezoidal bases and the lateral surfaces.
1.What are the types of surface areas in a trapezoidal prism?
2.How is the area of a trapezoidal base calculated?
3.How is the lateral surface area calculated?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Trapezoidal Prism
Students often make mistakes while calculating the surface area of a trapezoidal prism, which leads to incorrect answers. Below are some common mistakes and ways to avoid them.
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Seyed Ali Fathima S
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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.
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