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100 LearnersLast updated on December 11, 2025
Lateral Surface Area of a Triangular Pyramid
A triangular pyramid consists of four triangular faces, including a base and three lateral faces. The lateral surface area represents the total area of the three triangular faces that are not the base. Let's take an example of a tent. The fabric covering the sides of the tent forms the lateral surface, while the base is not included in the lateral surface area.
What is the Lateral Surface Area of a Triangular Pyramid?
The lateral surface area of a triangular pyramid is the sum of the areas of its lateral triangular faces.
It excludes the base area of the pyramid.
Formula for Lateral Surface Area of a Triangular Pyramid
To find the lateral surface area of a triangular pyramid, calculate the area of each of the three lateral triangular faces and sum them up.
If all side faces are congruent, you can use the formula: Area = (Perimeter of the base × Slant height) / 2
In cases where the slant height is not provided but the heights of the lateral triangles are known, calculate each triangle's area individually and add them up.
How to Find Lateral Surface Area of a Triangular Pyramid
To find the lateral surface area of a triangular pyramid, follow these steps:
Step 1: Identify the dimensions of each lateral triangular face.
Step 2: Ensure that all measurements are in the same unit.
Step 3: Calculate the area of each lateral triangular face.
Step 4: Sum the areas of the lateral faces to determine the total lateral surface area.
Step 5: Provide the calculated answer in square units.
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Tips and Tricks to Master Lateral Surface Area of a Triangular Pyramid
Here are some helpful strategies and advice to ensure the correct evaluation of the lateral surface area of a triangular pyramid:
- Verify the dimensions and ensure they are consistent across all calculations.
- When given the base perimeter and slant height, use the simplified formula for efficiency.
- In problems where the lateral faces are not congruent, calculate each face's area separately for accuracy.
- Practice with various problems to understand different scenarios and improve problem-solving skills.
- Avoid rounding values in intermediate steps to maintain accuracy.
Common Mistakes and How to Avoid Them in the Lateral Surface Area of a Triangular Pyramid
There are some typical mistakes people make while calculating the lateral surface area of a triangular pyramid.
Some of them are listed below:
Mistake 1
Confusing the base area with lateral surface area.
The base area of a triangular pyramid is not included in the lateral surface area.
Ensure you only calculate the areas of the lateral triangular faces.
Mistake 2
Incorrect area calculations of triangular faces.
Errors can occur when calculating the area of each triangular face.
Double-check calculations and ensure the correct application of the area formula for triangles.
Mistake 3
Not using consistent units.
Always ensure that all measurements are in the same units before performing calculations.
This prevents errors in the final area calculation.
Mistake 4
Rounding values in intermediate calculations.
Avoid rounding numbers until the final calculation to ensure accuracy in the final result.
Rounding intermediate values can lead to significant errors.
Mistake 5
Assuming all lateral faces are congruent without verification.
Verify if the lateral triangular faces are indeed congruent before using the simplified formula.
If not, calculate each face's area separately.
Solved Examples on Lateral Surface Area of a Triangular Pyramid
Problem 1
What is the lateral surface area of a triangular pyramid with side triangles each having a base of 5 cm and a height of 8 cm?
60 cm²
Explanation
Each triangular face has an area of: Area = (Base × Height) / 2 = (5 × 8) / 2 = 20 cm², Since there are three identical lateral faces, the LSA = 3 × 20 = 60 cm²
Problem 2
If the perimeter of the triangular base is 18 cm and the slant height is 7 cm, find the lateral surface area of the triangular pyramid.
63 cm²
Explanation
Using the formula: LSA = (Perimeter × Slant height) / 2 = (18 × 7) / 2 = 63 cm²
Problem 3
Calculate the lateral surface area of a triangular pyramid with three lateral triangles having bases of 4 cm, 6 cm, and 5 cm, with respective heights of 5 cm, 3 cm, and 4 cm.
41 cm²
Explanation
Area of each face:
Face 1: (4 × 5) / 2 = 10 cm²
Face 2: (6 × 3) / 2 = 9 cm²
Face 3: (5 × 4) / 2 = 10 cm²
LSA = 10 + 9 + 10 = 29 cm²
Problem 4
Find the height of a triangular pyramid if its lateral surface area is 84 cmยฒ and the perimeter of its base is 14 cm, with the slant height being 6 cm.
Height of a triangular pyramid = 6 cm.
Explanation
Given: Lateral surface area = 84 cm², Perimeter of base = 14 cm
Using the formula: LSA = (Perimeter × Slant height) / 2
84 = (14 × 6) / 2, Since the slant height is used and confirmed, the height remains as given, 6 cm.
Problem 5
The lateral surface area of a triangular pyramid is 96 cmยฒ. If the base perimeter is 16 cm, find its slant height.
12 cm
Explanation
Using the formula: LSA = (Perimeter × Slant height) / 2
96 = (16 × l) / 2
l = (96 × 2) / 16 = 12 cm
FAQโs on Lateral Surface Area of a Triangular Pyramid
1.What is Lateral Surface Area?
2.How to calculate the lateral surface area.
3.Is the lateral surface area and the total surface area the same?
4.What is the relation between slant height and lateral surface area?
5.How does the lateral surface area change if the base perimeter is doubled?
Important Glossary for Lateral Surface Area
- Triangular Pyramid: A solid object with triangular faces and a triangular base.
- Lateral Face: The triangular faces of a pyramid not including the base.
- Perimeter: The total length around a two-dimensional shape.
- Slant Height: The height from the base to the apex along a lateral face.
- Area of a Triangle: Calculated as (Base × Height) / 2 for any given triangle.
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
