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102 LearnersLast updated on September 4, 2025
Surface Area of Rectangular Pyramid
A rectangular pyramid is a 3-dimensional shape with a rectangular base and triangular faces that meet at a common point called the apex. The surface area of the rectangular pyramid is the total area covered by its outer surface. This includes the area of its base and the area of its triangular faces. In this article, we will learn about the surface area of a rectangular pyramid.
What is the Surface Area of a Rectangular Pyramid?
The surface area of a rectangular pyramid is the total area occupied by the boundary or surface of a rectangular pyramid. It is measured in square units.
A rectangular pyramid is a 3D shape with a rectangle as its base and four triangular faces that converge at the apex.
The surface area includes the area of the base and the lateral area formed by the triangular faces. Rectangular pyramids can vary based on the dimensions of their base and height, affecting their overall shape and surface area.
Surface Area of a Rectangular Pyramid Formula
A rectangular pyramid has a rectangular base and triangular faces. The surface area includes the base area and the lateral area formed by the triangular faces.
Look at the rectangular pyramid below to see its surface area, base dimensions (length l and width w), height (h), and slant heights.
A rectangular pyramid has two main components:
- Base Area of the Rectangular Pyramid
- Lateral Surface Area of the Rectangular Pyramid
Base Area of a Rectangular Pyramid
The area of the rectangular base of the pyramid is known as the base area.
The formula for the base area of a rectangular pyramid is given as: Base Area = l × w square units
Here, l is the length of the base, and w is the width of the base.
Lateral Surface Area of a Rectangular Pyramid
The lateral surface area is the total area of the triangular faces of the pyramid. It is calculated by finding the area of each triangular face and summing them up. The formula for the lateral surface area of a rectangular pyramid is given as:
Lateral Surface Area = ½ × perimeter of base × slant height
The perimeter of the base is the sum of all the sides of the rectangle, and the slant height is measured from the apex to the midpoint of a side of the base.
Total Surface Area of a Rectangular Pyramid
The total surface area of a rectangular pyramid is the sum of the base area and the lateral surface area. The formula is:
Total Surface Area = Base Area + Lateral Surface Area
Total Surface Area = l × w + ½ × perimeter of base × slant height
Confusion between Base Area and Lateral Surface Area
Students assume that the base area and the lateral surface area are the same. Always remember that the base area is the area of the rectangular base, while the lateral surface area includes the triangular faces.
Mistake 1
Using height instead of slant height
Some students mistakenly use the vertical height (h) instead of the slant height when finding the lateral surface area. Remember the formula for lateral surface area involves the slant height.
Mistake 2
Incorrect calculation of the perimeter
A common mistake is calculating the perimeter of the base incorrectly. Ensure you add all the sides of the rectangle to find the perimeter accurately.
Mistake 3
Forgetting to include the base area in the total surface area
Students often calculate only the lateral surface 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 4
Assuming all triangular faces are the same
Some students mistakenly believe all triangular faces are identical, but this can vary depending on the dimensions of the base. Calculate each triangular face individually if necessary.
Mistake 5
Solved Examples of Surface Area of Rectangular Pyramid
Find the lateral surface area of a rectangular pyramid with a base of length 8 cm, width 6 cm, and a slant height of 10 cm.
Lateral Surface Area = 280 cm²
Problem 1
Perimeter of base = 2(l + w) = 2(8 + 6) = 28 cm Lateral Surface Area = ½ × perimeter of base × slant height = ½ × 28 × 10 = 140 cm²
Find the total surface area of a rectangular pyramid with a base length of 5 cm, width of 4 cm, and slant height of 9 cm.
Explanation
Total Surface Area = 130 cm²
Problem 2
Base Area = l × w = 5 × 4 = 20 cm² Perimeter of base = 2(5 + 4) = 18 cm Lateral Surface Area = ½ × perimeter of base × slant height = ½ × 18 × 9 = 81 cm² Total Surface Area = Base Area + Lateral Surface Area = 20 + 81 = 101 cm²
A rectangular pyramid has a base of 12 cm by 9 cm and a slant height of 15 cm. Find the total surface area.
Explanation
Total Surface Area = 396 cm²
Problem 3
Base Area = l × w = 12 × 9 = 108 cm² Perimeter of base = 2(12 + 9) = 42 cm Lateral Surface Area = ½ × perimeter of base × slant height = ½ × 42 × 15 = 315 cm² Total Surface Area = Base Area + Lateral Surface Area = 108 + 315 = 423 cm²
Find the base area of a rectangular pyramid with a length of 7 cm and a width of 6 cm.
Explanation
Base Area = 42 cm²
Problem 4
Base Area = l × w = 7 × 6 = 42 cm²
The lateral surface area of a rectangular pyramid is 160 cm². Its base has a perimeter of 20 cm and a slant height of 8 cm. Find the length and width of the base.
Explanation
Length + Width = 10 cm
It is the total area that covers the outside of the rectangular pyramid, including its base and the lateral triangular faces.
1.What are the two main components of surface area in a rectangular pyramid?
2.What is the difference between slant height and height?
3.Is lateral surface area the same as the total surface area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Rectangular Pyramid
Students often make mistakes while calculating the surface area of a rectangular pyramid, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
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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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: She has songs for each table which helps her to remember the tables
