106 LearnersLast updated on August 30, 2025
Surface Area of an Isosceles Triangular Prism
An isosceles triangular prism is a 3-dimensional shape with two identical isosceles triangles as its bases and three rectangular faces connecting the corresponding sides of the triangles. The surface area of the prism is the total area covered by its outer surfaces, including the two triangular bases and the three rectangular lateral faces. In this article, we will learn about the surface area of an isosceles triangular prism.
What is the Surface Area of an Isosceles Triangular Prism?
The surface area of an isosceles triangular prism is the total area occupied by the boundary or surface of the prism.
It is measured in square units.
A prism is a 3D shape with two parallel, congruent bases.
In an isosceles triangular prism, these bases are isosceles triangles, meaning they have two equal sides and equal angles.
The surface area of the prism includes the areas of its two triangular bases and the lateral faces, which are rectangles.
Surface Area of an Isosceles Triangular Prism Formula
An isosceles triangular prism has lateral faces and two types of surface areas: the lateral surface area and the total surface area.
Look at the prism below to see its surface area, height (h), base length (b), side length (s), and prism height (ph).
A prism has two types of surface areas:
Lateral Surface Area of an Isosceles Triangular Prism
Total Surface Area of an Isosceles Triangular Prism
Lateral Surface Area of an Isosceles Triangular Prism
The lateral surface area is the sum of the areas of the three rectangular faces connecting the corresponding sides of the triangular bases.
The formula for the LSA (Lateral Surface Area) of the prism is given as:
Lateral Surface Area = ph(b + 2s) square units
Here, b is the base length of the triangular base. s is the equal side length of the triangular base. ph is the height of the prism.
Total Surface Area of an Isosceles Triangular Prism
The total surface area of the prism includes the lateral surface area and the areas of the two triangular bases.
The total surface area of an isosceles triangular prism is calculated by using the formula:
Total Surface Area = 2 × Area of triangular base + Lateral Surface Area
The area of a triangular base = ½ × b × h Where b is the base of the triangular base, and h is the height of the triangular base.
Substituting the formulas into the total surface area,
Total Surface Area, T = 2 × ½ × b × h + ph(b + 2s)
Volume of an Isosceles Triangular Prism
The volume of an isosceles triangular prism shows how much space is inside it. It tells us how much space the prism can hold.
The volume of a prism can be found by using the formula: Volume = Area of triangular base × prism height Volume = ½ × b × h × ph (cubic units)
Confusion between LSA and TSA
Students assume that the lateral surface area (LSA) and the total surface area (TSA) of a prism are the same.
This confusion arises because both involve the base length and side length.
Always remember that LSA includes only the lateral faces, while TSA includes both the lateral faces and the bases.
Mistake 1
Using only one base area for total surface area
Some students calculate the area of only one triangular base and forget to double it for the total surface area. Remember the formula for total surface area includes 2 × area of the triangular base.
Mistake 2
Incorrect use of measurements
A common mistake is using incorrect measurements for the sides of the triangle or the height of the prism. Always use accurate values and check which dimension each variable represents.
Mistake 3
Confusing base height with prism height
Students often confuse the height of the triangular base with the height of the prism. Ensure you use base height for the area of the triangle and prism height for the lateral surface area.
Mistake 4
Assuming all prism sides are equal
Some students mistakenly assume all sides of the prism are equal, especially when dealing with the triangular base. Remember, an isosceles triangle has only two equal sides. Use the correct side measurements.
Mistake 5
Solved Examples of Surface Area of an Isosceles Triangular Prism
Find the lateral surface area of an isosceles triangular prism with a base length of 5 cm, side length of 8 cm, and prism height of 12 cm.
LSA = 252 cm²
Problem 1
Given b = 5 cm, s = 8 cm, ph = 12 cm. Use the formula: LSA = ph(b + 2s) = 12 × (5 + 16) = 12 × 21 = 252 cm²
Find the total surface area of an isosceles triangular prism with base length 6 cm, base height 4 cm, and side length 7 cm, and prism height of 10 cm.
Explanation
TSA = 208 cm²
Problem 2
Area of one triangular base = ½ × b × h = ½ × 6 × 4 = 12 cm² Total surface area = 2 × 12 + 10 × (6 + 14) = 24 + 200 = 224 cm²
An isosceles triangular prism has a base length of 9 cm, a height of the base of 5 cm, and a prism height of 15 cm. Find the total surface area.
Explanation
TSA = 375 cm²
Problem 3
Area of one triangular base = ½ × 9 × 5 = 22.5 cm² Total surface area = 2 × 22.5 + 15 × (9 + 18) = 45 + 405 = 450 cm²
Find the lateral surface area of an isosceles triangular prism with a base of 7 cm, side length of 10 cm, and prism height of 8 cm.
Explanation
LSA = 352 cm²
Problem 4
LSA = ph(b + 2s) = 8 × (7 + 20) = 8 × 27 = 216 cm²
The prism height of an isosceles triangular prism is 18 cm, and the lateral surface area is 540 cm². Find the base length if the side length is 15 cm.
Explanation
Base length = 10 cm
It is the total area that covers the outside of the prism, including its lateral faces and the two triangular bases.
1.What are the two types of surface area in a prism?
2.What is the difference between base height and prism height?
3.Is the lateral surface area the same as the lateral faces' area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of an Isosceles Triangular Prism
Students often make mistakes while calculating the surface area of an isosceles triangular prism, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
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
