Perimeter of Right Prism
2026-02-28 11:16 Diff
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Last updated on September 8, 2025

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.

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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:

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.

Okay, lets begin

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.

Well explained 👍

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.

Okay, lets begin

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.

Well explained 👍

Problem 3

Find the perimeter of an equilateral triangular base of a right prism where each side is 10 cm.

Okay, lets begin

30 cm

Explanation

Perimeter of triangle = a + b + c

P = 10 + 10 + 10 = 30

Therefore, the perimeter of the triangular base is 30 cm.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of the base of a right prism where the triangular base has sides a = 10, b = 8, c = 7.

Okay, lets begin

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.

Well explained 👍

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.

Perimeter of rectangle = 2a + 2b. Hence P = 2(3) + 2(4) = 6 + 8 = 14 cm.

2.What is meant by the perimeter of a right prism?

The perimeter of a right prism refers to the total length around the base of the prism. It is the sum of the lengths of all sides of the base shape.

3.What are the types of base shapes that can form a right prism?

Common base shapes for right prisms include rectangular, triangular, hexagonal, and any other polygonal shapes.

4.Which base shape of a prism has no equal sides?

A scalene triangular base is a triangular shape with no equal sides. All three sides of a scalene triangle are different.

5.Which base shape of a prism typically has the smallest perimeter?

A base shape with the smallest perimeter for a given area is typically an equilateral triangle.

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