Summarize this article:
100 LearnersLast updated on September 17, 2025
Area of Pyramid
Area is the space inside the boundaries of a two-dimensional shape or surface. There are different formulas for finding the area of various shapes/figures. These are widely used in architecture and design. In this section, we will find the area of the pyramid.
What is the Area of Pyramid?
A pyramid is a three-dimensional shape with a polygonal base and triangular faces that converge at a single point called the apex.
The area of a pyramid includes its base area and the lateral surface area, which is the sum of the areas of its triangular faces.
Area of the Pyramid Formula
To find the total surface area of a pyramid, we calculate the base area and the lateral surface area. The total surface area is given by:
Total Surface Area = Base Area + Lateral Surface Area. Let's see how these components are determined.
Base Area: The base area depends on the shape of the base. For example, if the base is a square with side length 's', then the base area is s².
Lateral Surface Area: The lateral surface area is the sum of the areas of the triangular faces. For a pyramid with a square base, the lateral surface area is 1/2 × perimeter of base × slant height. Therefore, Total Surface Area = Base Area + 1/2 × Perimeter of Base × Slant Height
How to Find the Area of Pyramid?
We can find the area of the pyramid using specific methods, based on its base shape. The area of the pyramid is found using these steps:
1. Determine the base area based on its shape.
2. Calculate the lateral surface area using the slant height and base perimeter.
3. Add the base area to the lateral surface area for the total surface area.
Example for a Pyramid with a Square Base: If the side of the square base is 6 cm and the slant height is 10 cm, the base area is 6 × 6 = 36 cm².
The perimeter of the base is 4 × 6 = 24 cm. The lateral surface area is 1/2 × 24 × 10 = 120 cm². Therefore, the total surface area is 36 + 120 = 156 cm².
Unit of Area of Pyramid
We measure the area of a pyramid in square units. The measurement depends on the system used:
In the metric system, the area is measured in square meters (m²), square centimeters (cm²), and square millimeters (mm²).
In the imperial system, the area is measured in square inches (in²), square feet (ft²), and square yards (yd²).
Special Cases or Variations for the Area of Pyramid
The method for calculating the area of a pyramid can change based on the shape of its base. Here are some special cases:
Case 1: Pyramid with a Square Base For a square base, calculate the base area as s² and the lateral surface area as 1/2 × perimeter of base × slant height.
Case 2: Pyramid with a Rectangular Base For a rectangular base, the base area is length × width, and the lateral surface area is calculated using the slant heights of the triangular faces.
Case 3: Pyramid with a Triangular Base Use the formula for the area of a triangle for the base area and add the lateral areas of the other triangles.
Tips and Tricks for Area of Pyramid
To ensure accuracy when calculating the area of a pyramid, consider these tips and tricks:
- Ensure correct measurement of the slant height, as it differs from the height of the pyramid.
- The base area calculation depends on the shape of the base. Use the appropriate formula for the base.
- Confirm the correct units are used for all measurements to maintain consistency.
Common Mistakes and How to Avoid Them in Area of Pyramid
It is common for students to make mistakes while finding the area of a pyramid. Let’s take a look at some mistakes made by students.
Mistake 1
Using the height instead of the slant height
To find the lateral surface area, use the slant height, not the vertical height of the pyramid.
The lateral surface area formula requires the slant height.
Mistake 2
Measuring the area using inappropriate units
For the area to be in square meters (m²), all measurements should be in meters.
Convert units if necessary to ensure uniformity.
Mistake 3
Confusing Base Area Calculation
Ensure the base area is calculated using the correct formula for the specific shape of the base, such as a square or rectangle.
Mistake 4
Incorrect Perimeter Calculation
The perimeter should reflect the actual base shape dimensions.
For a square base, the perimeter is 4 times the side length.
Mistake 5
Neglecting to Add Base Area to Lateral Surface Area for Total Area
Remember to add the base area to the lateral surface area to get the total surface area of the pyramid.
Area of Pyramid Examples
Problem 1
A pyramid has a square base with a side length of 8 m and a slant height of 12 m. What is the total surface area?
We will find the total surface area as 272 m².
Explanation
The base area is 8 × 8 = 64 m².
The perimeter of the base is 4 × 8 = 32 m.
The lateral surface area is 1/2 × 32 × 12 = 192 m².
The total surface area is 64 + 192 = 272 m².
Problem 2
What will be the area of a pyramid with a rectangular base measuring 5 cm by 10 cm and a slant height of 7 cm?
We will find the total surface area as 135 cm².
Explanation
The base area is 5 × 10 = 50 cm².
The perimeter of the base is 2(5 + 10) = 30 cm.
The lateral surface area is 1/2 × 30 × 7 = 105 cm².
The total surface area is 50 + 105 = 155 cm².
Problem 3
A triangular pyramid has a base with sides of 6 m each and a slant height of 8 m. What is the total surface area?
We find the total surface area as 103.92 m².
Explanation
The base area is (sqrt(3)/4)s² = (sqrt(3)/4)(6)² = 15.59 m².
The perimeter of the base is 3 × 6 = 18 m.
The lateral surface area is 1/2 × 18 × 8 = 72 m².
The total surface area is 15.59 + 72 = 87.59 m².
Problem 4
Find the area of a pyramid with a hexagonal base where each side of the base is 4 cm and the slant height is 9 cm.
We will find the total surface area as 155.88 cm².
Explanation
The base area is (3√3/2)s² = (3√3/2)(4)² = 41.57 cm².
The perimeter of the base is 6 × 4 = 24 cm.
The lateral surface area is 1/2 × 24 × 9 = 108 cm².
The total surface area is 41.57 + 108 = 149.57 cm².
Problem 5
Help Sarah find the area of a pyramid with a pentagonal base, side length of 3 m, and slant height of 5 m.
We will find the total surface area as 82.53 m².
Explanation
The base area is (5/4)√(5(5+2√5)) × s² = 15.48 m².
The perimeter of the base is 5 × 3 = 15 m.
The lateral surface area is 1/2 × 15 × 5 = 37.5 m².
The total surface area is 15.48 + 37.5 = 52.98 m².
FAQs on Area of Pyramid
1.Is it possible for the area of a pyramid to be negative?
2.How to find the area of a pyramid if the slant height and base dimensions are given?
3.How to find the area of a pyramid if only base perimeter is given?
4.How is the volume of a pyramid calculated?
5.What is meant by the area of the pyramid?
Glossary of Terms Related to Area of Pyramid
- Base Area: The area of the base polygon of the pyramid.
- Lateral Surface Area: The sum of the areas of the triangular faces that connect the base to the apex.
- Slant Height: The height of each triangular face from the base to the apex.
- Total Surface Area: The sum of the base area and the lateral surface area.
- Perimeter: The total length around the boundary of a polygonal base.
Explore More measurement
![Important Math Links Icon]()
Previous to Area of Pyramid
![Important Math Links Icon]()
Next to Area of 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
