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128 LearnersLast updated on September 4, 2025
Surface Area of Pyramid
A pyramid is a 3-dimensional shape with a polygonal base and triangular faces that converge at a single point called the apex. The surface area of a pyramid is the total area covered by its outer surface, including the base and the triangular faces. In this article, we will learn about the surface area of a pyramid.
What is the Surface Area of a Pyramid?
The surface area of a pyramid is the total area occupied by its boundary or surface. It is measured in square units.
A pyramid has a polygonal base and triangular faces that connect the base to the apex.
The surface area of a pyramid includes the area of the base and the lateral surface area, which is the sum of the areas of the triangular faces.
Pyramids can have different types of bases, such as square, rectangular, or other polygons.
Surface Area of a Pyramid Formula
A pyramid has a base and triangular faces, and its surface area consists of two parts: the base area and the lateral surface area.
Look at the pyramid below to see its surface area, slant height (l), and base perimeter (P).
A pyramid has two components of surface area:
- Base Area of the Pyramid
- Lateral Surface Area of the Pyramid
Lateral Surface Area of a Pyramid
The lateral surface area of a pyramid is the total area of the triangular faces, excluding the base.
The formula for the lateral surface area (LSA) of a pyramid is given as: Lateral Surface Area = 1/2 x P x l square units
Here, P is the perimeter of the base of the pyramid. l is the slant height of the pyramid.
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Total Surface Area of a Pyramid
The total area occupied by the pyramid, including the area of the base and the lateral surface area, is known as the total surface area of the pyramid.
The total surface area of a pyramid is calculated using the formula:
Total Surface Area = Base Area + Lateral Surface Area
To find the total surface area of a pyramid, calculate the area of the polygonal base and add it to the lateral surface area.
For example, if the base is a square with side length a, the base area is a2 .
Volume of a Pyramid
The volume of a pyramid shows how much space is inside it. It tells us how much space is inside the pyramid or how much it can hold.
The volume of a pyramid can be found using the formula: Volume = 1/3 x Base Area x h cubic units where h is the vertical height from the apex to the base.
Confusion between LSA and TSA
Students assume that the lateral surface area (LSA) and the total surface area (TSA) of a pyramid are the same. This confusion arises because both involve the slant height and the base perimeter. Always remember that LSA is only for the triangular faces, and TSA includes the base.
Mistake 1
Using height instead of slant height
Some students mistakenly use the vertical height (h) instead of the slant height (l) when finding the lateral surface area. Remember the formula for lateral surface area is \( \frac{1}{2} \times P \times l \), so always use the slant height.
Mistake 2
Forgetting to include the base area in the total surface area
Students often calculate only the lateral surface area and forget to add the base area. Always include both parts when calculating the total surface area: Total Surface Area = Base Area + Lateral Surface Area.
Mistake 3
Assuming lateral surface area and curved surface area are different
Some students mistakenly believe that lateral surface area and curved surface area are different, but in a pyramid, they mean the same thing. So, use the same formula for both.
Mistake 4
Solved Examples of Surface Area of Pyramid
Find the lateral surface area of a square pyramid with a base perimeter of 24 cm and a slant height of 10 cm.
LSA = 120 cm²
Problem 1
Given P = 24 cm, l = 10 cm. Use the formula: LSA = \( \frac{1}{2} \times P \times l \) = \( \frac{1}{2} \times 24 \times 10 \) = 12 × 10 = 120 cm²
Find the total surface area of a square pyramid with a base side length of 6 cm and a slant height of 8 cm.
Explanation
TSA = 180 cm²
Problem 2
The base area = 6 x 6 = 36 cm² The base perimeter P = 4 x 6 = 24 cm Use the formula: LSA = 1/2 x P l = 1/2 x 24 8 = 96 cm² Total Surface Area = Base Area + LSA = 36 + 96 = 132 cm²
A triangular pyramid has a base perimeter of 30 cm and a slant height of 12 cm. Find the lateral surface area.
Explanation
LSA = 180 cm²
Problem 3
Given P = 30 cm, l = 12 cm. Use the formula: LSA = \( \frac{1}{2} \times P \times l \) = \( \frac{1}{2} \times 30 \times 12 \) = 15 × 12 = 180 cm²
Find the total surface area of a triangular pyramid with base area 20 cm², base perimeter 15 cm, and slant height 5 cm.
Explanation
TSA = 57.5 cm²
Problem 4
LSA = \( \frac{1}{2} \times P \times l \) = \( \frac{1}{2} \times 15 \times 5 \) = 37.5 cm² Total Surface Area = Base Area + LSA = 20 + 37.5 = 57.5 cm²
The slant height of a square pyramid is 14 cm, and its lateral surface area is 280 cm². Find the base perimeter.
Explanation
Base Perimeter = 40 cm
It is the total area that covers the outside of the pyramid, including its triangular faces and the base.
1.What are the two types of surface area in a pyramid?
2.What is the difference between slant height and height?
3.Is lateral surface area the same as curved surface area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Pyramid
Students often make mistakes while calculating the surface area of a pyramid, leading to wrong answers. Below are some common mistakes and 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.
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