Summarize this article:
104 LearnersLast updated on December 11, 2025
Lateral Surface Area of a Pyramid with Triangular Base
A pyramid with a triangular base consists of a triangular base and three triangular lateral faces. The lateral surface area represents the sum of the areas of these three triangular faces. Let's take an example of a tent. The fabric of the tent excluding the ground represents the lateral surface, which is equal to the lateral surface area of the pyramid. The base triangle is not included because it is on the ground.
What is the Lateral Surface Area of a Pyramid with a Triangular Base?
The lateral surface area of a pyramid with a triangular base is the sum of the areas of the three triangular faces that extend from the base to the apex.
Formula for Lateral Surface Area of a Pyramid with a Triangular Base
To find the lateral surface area of a pyramid with a triangular base, you need the slant heights of each triangular face and the lengths of the sides of the base triangle.
The lateral surface area is calculated by summing the areas of the individual triangular faces:
Area = 1/2 × (base1 × slant height1 + base2 × slant height2 + base3 × slant height3).
How to Find Lateral Surface Area of a Pyramid with a Triangular Base
To find the Lateral Surface Area of a Pyramid with a Triangular Base, follow these steps:
Step 1: Take note of the given parameters, including base side lengths and slant heights.
Step 2: Ensure that all the measurements are in the same unit before the calculation.
Step 3: Use the equation, Area = 1/2 × (base1 × slant height1 + base2 × slant height2 + base3 × slant height3), to find the LSA of the pyramid.
Step 4: Provide the calculated answer in square units.
Explore Our Programs
Common mistakes and how to avoid them in the Lateral Surface Area of a Pyramid with a Triangular Base.
There are a few typical mistakes people make while calculating the lateral surface area of a pyramid with a triangular base.
Some of them are listed below:
Mistake 1
Misinterpretation of the height of the pyramid as the slant height.
It's a very basic mistake students make.
The height of the pyramid is the perpendicular distance from the base to the apex.
In contrast, the slant height is the distance along the face from the base to the apex.
Mistake 2
Incorrectly calculating the area of each triangular face.
A simple yet common mistake occurs when using incorrect base side lengths or slant heights.
Ensure the correct values are used for each triangular face area calculation.
Mistake 3
Not mentioning the units with the numerical value.
It's important to mention the unit with the answer, even if the question doesn't specify the unit.
It's preferable to write “square units” as a unit for the standard representation of a value.
Mistake 4
Rounding in earlier steps.
Even though rounding is done correctly in earlier steps, it can make a big difference in the answer.
Hence, round off the final answer to the required number of decimal places.
Mistake 5
Confusing lateral surface area with total surface area.
Lateral surface area is the region occupied by the triangular faces, while the total surface area includes both the area covered by the triangular faces and the base of the pyramid.
Solved examples on Lateral Surface Area of a Pyramid with a Triangular Base
Problem 1
What is the lateral area of a pyramid with a triangular base having side lengths of 3 cm, 4 cm, and 5 cm, and slant heights of 6 cm for each face?
54 cm²
Explanation
Given: Base sides = 3 cm, 4 cm, 5 cm Slant heights = 6 cm each
LSA = 1/2 × (3×6 + 4×6 + 5×6) = 1/2 × (18 + 24 + 30) = 1/2 × 72 = 36 cm²
Problem 2
If the base of a triangular pyramid has sides of 5 cm, 5 cm, and 8 cm, with corresponding slant heights of 7 cm, 7 cm, and 9 cm, find the lateral surface area.
85 cm²
Explanation
Given: Base sides = 5 cm, 5 cm, 8 cm Slant heights = 7 cm, 7 cm, 9 cm
LSA = 1/2 × (5×7 + 5×7 + 8×9) = 1/2 × (35 + 35 + 72) = 1/2 × 142 = 71 cm²
Problem 3
Calculate the lateral surface area of a pyramid with a triangular base where each side is 6 cm, and the slant height for each face is 10 cm.
90 cm²
Explanation
Given: Base sides = 6 cm each Slant height = 10 cm for each face
LSA = 1/2 × (6×10 + 6×10 + 6×10) = 1/2 × 180 = 90 cm²
Problem 4
Evaluate the slant heights necessary for a pyramid with a triangular base of sides 4 cm, 6 cm, and 7 cm to have a lateral surface area of 100 square units, assuming equal slant heights.
8.33 units
Explanation
Given: Base sides = 4 cm, 6 cm, 7 cm LSA = 100 square units
Equal slant heights = l units
LSA = 1/2 × (4l + 6l + 7l) = 100
1/2 × 17l = 100 17l = 200
l = 200/17 = 11.76 units
Problem 5
The lateral surface area of a pyramid with a triangular base is 75 cmยฒ. If the base has sides of 3 cm, 4 cm, and 5 cm, find the average slant height.
5 cm
Explanation
Average slant height = Total LSA / Total base perimeter
Given: Base sides = 3 cm, 4 cm, 5 cm, LSA = 75 cm²
Perimeter = 3 + 4 + 5 = 12 cm
Average slant height = 75/12 = 6.25 cm
FAQโs on Lateral Surface Area
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.How do slant heights affect the lateral surface area?
5.Does the base shape affect the lateral surface area?
Important Glossary for Lateral Surface Area
- Slant height: The height of a triangular face from the base to the apex.
- Base: The triangle at the bottom of the pyramid.
- Apex: The topmost point where all triangular faces meet.
- Perimeter: The total length around the base of the pyramid.
- Triangular face: Each of the three triangles forming the sides of the pyramid.
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
