105 LearnersLast updated on July 29th, 2025
Perimeter of Prism
The perimeter of a shape is the total length of its boundary. In the context of a prism, the perimeter can refer to the perimeter of the base shape of the prism. Perimeter is often used in practical situations like fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a prism.
What is the Perimeter of a Prism?
The perimeter of a prism refers to the perimeter of its base shape. For example, if the base of a prism is a triangle, the perimeter is the total length of its three sides. If the base is a rectangle, it is the sum of all four sides. The formula for the perimeter depends on the shape of the prism's base. For instance, if a triangular prism has a base with sides a = 6, b = 8, and c = 10, then its base perimeter is P = 6 + 8 + 10 = 24.
Formula for Perimeter of Prism Base
Let’s consider an example of a rectangular prism with a base of length l = 8 and width w = 10. The perimeter of the rectangular base will be: P = 2(l + w) = 2(8 + 10) = 36.
How to Calculate the Perimeter of Prism Base
To find the perimeter of a prism's base, apply the formula according to the shape of the base and sum all the sides. For instance, for a rectangular base with length l = 6 and width w = 4, the perimeter is P = 2(l + w) = 2(6 + 4) = 20. Example Problem on Perimeter of Prism Base - For finding the perimeter of a triangular base, use the formula P = a + b + c. For example, let’s say a triangular base has sides a = 5 cm, b = 4 cm, and c = 2 cm. Now, the perimeter = sum of all sides = 5 + 4 + 2 = 11 cm. Therefore, the perimeter of the triangle is 11 cm.
Tips and Tricks for Perimeter of Prism Base
Learning some tips and tricks makes it easier to calculate the perimeter of prism bases. Here are some tips and tricks given below: Always remember that the perimeter of a prism's base is simply the sum of the sides of its base shape. Use the appropriate formula for the shape. Calculating the perimeter starts by determining the length of each side of the base using known values or formulas. For example, for a rectangular base, use P = 2(l + w). To reduce confusion, specifically arrange the side lengths of the base if you need the perimeter of multiple prisms. After that, apply the formula to each prism base. To avoid mistakes when adding the perimeter, make sure the side lengths are precise and consistent for common uses like construction and design. If you are given the semi-perimeter of the base, which is half the perimeter, multiply it by 2 to determine the full perimeter. This can be useful in certain area-related calculations.
Common Mistakes and How to Avoid Them in Perimeter of Prism Base
Did you know that while working with the perimeter of a prism's base, people might encounter some errors or difficulties? Here are some common mistakes and solutions:
Mistake 1
Incorrectly using base perimeter formulas for different shapes.
Ensure you use the correct formula based on the shape of the prism's base. For instance, use P = 2(l + w) for rectangles and P = a + b + c for triangles.
Mistake 2
Confusing the concepts of area and perimeter, leading to incorrect calculations.
Remember that the perimeter, calculated in linear units, is the total length around the base, while the area measures the space inside.
Mistake 3
Assuming all prisms have the same base shape, leading to inaccurate calculations.
Prisms can have different base shapes, such as triangular, rectangular, or polygonal. Always verify the base shape before calculating the perimeter.
Mistake 4
Using the wrong values for the length of the sides, misreading a problem, or mislabeling the sides.
Double-check the problem and ensure that you're using the correct lengths for the prism base.
Mistake 5
Misunderstanding or misidentifying the side lengths given in a problem outline.
Before starting the calculations, make sure you understand the problem and, if possible, sketch the base shape to accurately identify the side lengths.
Perimeter of Prism Examples
Problem 1
A triangular prism has a triangular base with two sides measuring 17 inches each and a perimeter of 48 inches. To find out the missing side of the base, subtract the sum of the known sides from the total perimeter.
Length of the missing side = 14 inches.
Explanation
Let ‘b’ be the length of the missing side. And the given perimeter = 48 inches. Length of the two equal sides = 17 inches. Perimeter of triangle = sum of lengths of three sides. 48 = 17 + 17 + b 48 = 34 + b b = 48 – 34 = 14 b = 14 Therefore, the missing side is 14 inches.
Problem 2
A wire with a length of 297 inches is reshaped into the perimeter of an equilateral triangle base of a prism. Find the length of each side of the triangle by dividing the total length by 3.
99 inches
Explanation
Given that the wire is reshaped into an equilateral triangle base, here is the solution: Perimeter of the equilateral triangle = 3 × a 297 = 3 × a 297 ÷ 3 = 99 a = 99 Therefore, the length of each side of the triangle is 99 inches.
Problem 3
Find the perimeter of an equilateral triangle base of a prism with sides measuring 10 cm.
30 cm
Explanation
Perimeter of triangle = a + b + c P = 10 + 10 + 10 = 30 Therefore, the perimeter of the triangle is 30 cm.
Problem 4
Annie is planning a rectangular vegetable garden in her backyard, which is a prism base. She measures the sides of the garden: Length = 12 meters Width = 9 meters How much string should Annie buy to go around the edge of the garden?
Annie will need 42 meters of string to go around the garden.
Explanation
The perimeter of a rectangle is the sum of all sides. Using the formula: P = 2(l + w) P = 2(12 + 9) = 42 meters.
Problem 5
Find the perimeter of the triangular base of a prism with sides of 10, 8, and 7 meters.
Perimeter = a + b + c = 10 + 8 + 7 = 25 meters.
Explanation
Each side of the triangular base has a different length. The total distance around the base is calculated by summing the lengths of the three sides, which is 25 meters.
FAQs on Perimeter of Prism Base
1.Evaluate the perimeter of a triangular base if its sides are 3 cm, 4 cm, and 6 cm.
2.What is meant by a prism base’s perimeter?
3.What are the types of prisms based on their bases?
4.Which shape has a base perimeter that can be calculated as 2(l + w)?
5.Which prism base has all equal side lengths?
Important Glossaries for Perimeter of Prism Base
Perimeter: The total length of the sides of a shape. Prism: A solid object with two identical ends and flat sides. Base: The face of the prism that determines its shape. Triangular base: A base in the shape of a triangle. Rectangular base: A base in the shape of a rectangle.
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
