101 LearnersLast updated on 30 August 2025
Surface Area of Right Triangular Pyramid
A right triangular pyramid is a 3-dimensional shape with a triangular base and three triangular faces that meet at a single point called the apex. The surface area of a right triangular pyramid is the total area covered by its outer surface. It includes the area of its base and the areas of its three triangular faces. In this article, we will explore the surface area of a right triangular pyramid.
What is the Surface Area of a Right Triangular Pyramid?
The surface area of a right triangular pyramid is the total area occupied by the boundary or surface of the pyramid.
It is measured in square units.
A right triangular pyramid has a triangular base and three triangular lateral faces that connect the base to the apex.
The surface area includes both the base area and the lateral surface area (the sum of the three triangular faces).
Surface Area of a Right Triangular Pyramid Formula
A right triangular pyramid has a triangular base, and it has two main parts contributing to the surface area: the base area and the lateral surface area.
Consider a right triangular pyramid with a base of area Ab and three lateral faces with areas A1, A2, and A3.
The surface area (SA) of a right triangular pyramid is given by: Surface Area = Base Area + Lateral Surface Area = Ab + A1 + A2 + A3
Base Area of a Right Triangular Pyramid
The base area of a right triangular pyramid is simply the area of its triangular base. If the triangle has a base length b and a height h, the base area (Ab) is calculated as: Base Area = (1/2) × b × h
Lateral Surface Area of a Right Triangular Pyramid
The lateral surface area of a right triangular pyramid is the sum of the areas of its three triangular lateral faces.
Each face can be calculated using the appropriate base and height for that triangle.
The lateral surface area (LSA) is given by: Lateral Surface Area = A1 + A2 + A3
Volume of a Right Triangular Pyramid
The volume of a right triangular pyramid represents the amount of space inside it. It is one-third of the product of the base area and the height of the pyramid (the perpendicular distance from the apex to the base).
The formula for volume is: Volume = (1/3) × Base Area × Height = (1/3) × Ab × h
Confusion between Base Area and Lateral Surface Area
Students sometimes mistakenly swap the base area with the lateral surface area. Always remember that the base area is calculated using the base of the triangular base, while the lateral surface area is the sum of the areas of the three triangular faces.
Mistake 1
Incorrect Calculation of Lateral Faces
Some students incorrectly calculate the areas of the lateral faces by not using the correct base and height for each triangular face. Ensure you correctly identify the base and height for each face to avoid errors.
Mistake 2
Misuse of Height in Volume Calculation
A common mistake is using the slant height instead of the perpendicular height when calculating the volume. Remember, the volume formula uses the perpendicular height from the apex to the base.
Mistake 3
Forgetting to Include All Triangular Faces
Students often forget to include one or more of the triangular faces in the lateral surface area calculation. Ensure all three faces are accounted for in your calculations.
Mistake 4
Assuming All Triangular Faces Are the Same
Some students assume that all the triangular faces of the pyramid are identical, leading to incorrect calculations. Check each face individually for accurate results.
Mistake 5
Solved Examples of Surface Area of Right Triangular Pyramid
Find the surface area of a right triangular pyramid with a base area of 24 cm² and lateral face areas of 15 cm², 18 cm², and 20 cm².
Surface Area = 77 cm²
Problem 1
Given A_b = 24 cm², A_1 = 15 cm², A_2 = 18 cm², A_3 = 20 cm². Use the formula: Surface Area = A_b + A_1 + A_2 + A_3 = 24 + 15 + 18 + 20 = 77 cm²
Find the base area of a right triangular pyramid with a base length of 6 cm and a height of 4 cm.
Explanation
Base Area = 12 cm²
Problem 2
Use the formula: Base Area = (1/2) × b × h = (1/2) × 6 × 4 = 12 cm²
A right triangular pyramid has a base area of 30 cm² and a perpendicular height of 9 cm. Find its volume.
Explanation
Volume = 90 cm³
Problem 3
Use the volume formula: Volume = (1/3) × A_b × h = (1/3) × 30 × 9 = (1/3) × 270 = 90 cm³
Find the lateral surface area of a right triangular pyramid with face areas of 10 cm², 12 cm², and 14 cm².
Explanation
Lateral Surface Area = 36 cm²
Problem 4
Lateral Surface Area = A_1 + A_2 + A_3 = 10 + 12 + 14 = 36 cm²
The base area of a right triangular pyramid is 50 cm² and its volume is 150 cm³. Find the perpendicular height.
Explanation
Height = 9 cm
It is the total area that covers the outside of the pyramid, including its triangular base and the three lateral triangular faces.
1.What are the two main parts of the surface area in a right triangular pyramid?
2.What is the difference between the slant height and the perpendicular height?
3.How do you calculate the base area of a right triangular pyramid?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Right Triangular Pyramid
Students often make mistakes while calculating the surface area of a right triangular pyramid, 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
