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104 LearnersLast updated on September 8, 2025
Perimeter of Right Prism
The perimeter of a shape is the total length of its boundary. When dealing with a right prism, the perimeter refers to the perimeter of its base, which is the sum of all the sides of the base shape. Perimeter is often used in various practical applications such as construction and design. In this topic, we will learn about the perimeter of a right prism.
What is the Perimeter of a Right Prism?
The perimeter of a right prism is the total length of the boundary of its base. By adding the lengths of all the sides of the base shape, we obtain the perimeter of the prism's base.
For instance, if the base of a right prism is a triangle with sides a = 6, b = 8, and c = 10, then the perimeter of the base is P = 6 + 8 + 10 = 24.
Formula for Perimeter of Right Prism Base
Let’s consider another example of a right prism with a rectangular base having side lengths a = 8, b = 10.
The perimeter of the rectangle, which is the base of the prism, will be: P = 2a + 2b = 2(8) + 2(10) = 16 + 20 = 36.
How to Calculate the Perimeter of Right Prism Base
To find the perimeter of a right prism's base, apply the relevant formula for the perimeter of the base shape.
For instance, if a given right prism has a rectangular base with sides a = 6 and b = 9, the perimeter of the base is P = 2a + 2b = 2(6) + 2(9) = 12 + 18 = 30 cm.
Example Problem on Perimeter of Right Prism Base -
To find the perimeter of the base of a right prism with a triangular base, we use the formula P = a + b + c.
For example, if the base is a triangle with sides a = 5 cm, b = 4 cm, and c = 2 cm, then the perimeter = sum of all sides = 5 + 4 + 2 = 11 cm.
Therefore, the perimeter of the base is 11 cm.
Tips and Tricks for Perimeter of Right Prism
Learning some tips and tricks can make it easier to calculate the perimeter of a right prism's base. Here are some tips and tricks:
- Always remember that the perimeter of the base of a prism is simply the sum of the lengths of all its sides.
- Use the appropriate formula based on the shape of the base. For a rectangular base, use P = 2a + 2b.
- For other shapes, use the relevant perimeter formula. When dealing with a right prism, ensure that you have correctly identified the shape and dimensions of the base before calculating the perimeter.
- For complex shapes, break down the base into simpler parts, calculate each part's perimeter, and sum them up. If given the semi-perimeter of the base, multiply it by 2 to find the full perimeter.
Common Mistakes and How to Avoid Them in Perimeter of Right Prism
While working with the perimeter of a right prism, some errors or difficulties may arise. Here are solutions to some common problems:
Mistake 1
Confusing the perimeter of the base with the surface area of the prism.
Remember, the perimeter is the total length around the base, not the surface area of the prism. The surface area involves all faces of the prism.
Mistake 2
Mixing up the formulas for different base shapes, leading to incorrect calculations.
Ensure you use the correct formula for the specific shape of the base. For instance, use P = 2a + 2b for rectangles and P = a + b + c for triangles.
Mistake 3
Assuming all bases are rectangular, which results in inaccurate calculations.
Not all right prisms have rectangular bases. Verify the shape of the base to ensure accurate calculations.
Mistake 4
Using incorrect values for side lengths, misreading a problem, or mislabeling the sides.
Double-check the problem and ensure that you're using the correct lengths for your prism's base.
Mistake 5
Misunderstanding or misidentifying the side lengths given in a problem outline.
Before starting calculations, make sure you understand the problem and, if possible, try to sketch the base to accurately identify the side lengths.
Perimeter of Right Prism Examples
Problem 1
A right prism has a rectangular base with a perimeter of 48 inches and two sides measuring 17 inches each. Find the length of the other side of the base.
Length of the missing side = 7 inches.
Explanation
Let ‘b’ be the missing side of the rectangle. Given perimeter = 48 inches. Length of the two equal sides = 17 inches.
Perimeter of rectangle = 2a + 2b. 48 = 2(17) + 2b 48 = 34 + 2b 2b = 48 – 34 = 14 b = 7
Therefore, the missing side is 7 inches.
Problem 2
A metal sheet with a perimeter of 297 inches is reshaped into a right prism with an equilateral triangular base. Find the length of each side of the base.
99 inches
Explanation
Given that the perimeter of the metal sheet is equal to the total length around the triangular base:
Perimeter of equilateral triangle = 3 × a
297 = 3 × a
297 ÷ 3 = 99
a = 99
Therefore, the length of each side of the triangular base is 99 inches.
Problem 3
Find the perimeter of an equilateral triangular base of a right prism where each side is 10 cm.
30 cm
Explanation
Perimeter of triangle = a + b + c
P = 10 + 10 + 10 = 30
Therefore, the perimeter of the triangular base is 30 cm.
Problem 4
Annie is planning a rectangular garden on the base of a right prism in her backyard. She measures the two sides of the garden: Side A = 12 meters Side B = 9 meters How much fencing should Annie buy to go around the edge of the garden?
Annie will need 42 meters of fencing to go around the garden.
Explanation
The perimeter of a rectangle is calculated by the formula: P = 2a + 2b P = 2(12) + 2(9) = 24 + 18 = 42 meters.
Problem 5
Find the perimeter of the base of a right prism where the triangular base has sides a = 10, b = 8, c = 7.
Perimeter = a + b + c = 10 + 8 + 7 = 25 meters.
Explanation
Each side of the triangular base of the right prism has a different length. The total perimeter is calculated by summing the lengths of the three sides, resulting in 25 meters.
FAQs on Perimeter of Right Prism
1.Evaluate the perimeter of the rectangular base of a right prism if its sides are 3 cm and 4 cm.
2.What is meant by the perimeter of a right prism?
3.What are the types of base shapes that can form a right prism?
4.Which base shape of a prism has no equal sides?
5.Which base shape of a prism typically has the smallest perimeter?
Important Glossaries for Perimeter of Right Prism
- Perimeter: The total length of the sides of a shape.
- Right Prism: A three-dimensional shape with two congruent bases and rectangular lateral faces.
- Base: The face of a prism that is used to define its perimeter and surface area.
- Formula for Perimeter of Base: The mathematical expression used to calculate the perimeter of the base shape, such as P = a + b + c for triangles or P = 2a + 2b for rectangles.
- Equilateral: A type of shape, particularly a triangle, where all sides are of equal length.
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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.
Fun Fact
: She has songs for each table which helps her to remember the tables
