108 LearnersLast updated on August 5th, 2025
Perimeter of Triangular Prism
The perimeter of a shape refers to the total length of its boundary. In a triangular prism, the perimeter involves the sum of the lengths of its triangular bases. Understanding the perimeter is essential for applications like material usage in construction. In this topic, we will learn about the perimeter of a triangular prism.
What is the Perimeter of a Triangular Prism?
The perimeter of a triangular prism is the sum of the lengths of its three edges on the triangular base. By adding the length of all three sides of the triangular base, we get the perimeter of that base. For example, if a triangular prism has a base with sides, a = 6, b = 8, and c = 10, then the perimeter of its base is P = 6 + 8 + 10 = 24.
Formula for Perimeter of Triangular Prism - P = a + b + c.
Consider another example of a triangular prism with base side lengths, a = 8, b = 10, and c = 12. The perimeter of the triangular base will be: P = a + b + c = 8 + 10 + 12 = 30.
How to Calculate the Perimeter of a Triangular Prism
To find the perimeter of the triangular base of a prism, apply the formula by summing all the sides of the triangle. For instance, given a triangular base with sides a = 6, b = 6, and c = 6, the perimeter = sum of all sides = 6 + 6 + 6 = 18 cm. Example Problem on Perimeter of Triangular Prism - For finding the perimeter of the triangular base of a prism, use the formula, P = a + b + c. For example, let’s say, 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 triangular base is 11 cm.
Tips and Tricks for Perimeter of Triangular Prism
Learning some tips and tricks makes it easier for children to calculate the perimeter of triangular bases in prisms. Here are some tips and tricks given below: Always remember that the perimeter of a triangular base in a prism is simply the sum of the three sides of the base. For that, use the formula, P = a + b + c. Calculating the perimeter of a triangular base starts by determining the length of each side using the distance formula if vertices are given. The distance formula is: Distance = √((x2-x1)² + (y2-y1)²). Here, (x1, y1) and (x2, y2) indicate the positions of two points that make up a side of the triangle. To reduce confusion, organize the indicated side lengths if you need the perimeter of multiple triangular bases. Then apply the formula to each base. To avoid mistakes when adding the perimeter, ensure the side lengths are precise and consistent for applications like construction and design. If you are given the semi-perimeter of a triangular base, which is half the perimeter, you can multiply it by 2 to determine the full perimeter.
Common Mistakes and How to Avoid Them in Perimeter of Triangular Prism
Did you know that while working with the perimeter of a triangular prism, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Incorrectly using the Pythagorean theorem (a² + b² = c²) for triangles that are not right-angled.
Remember that only right-angled triangles can use the Pythagorean theorem. The lengths of all the sides of other triangle types should be summed up to find the perimeter of the base.
Mistake 2
Students may confuse the concepts of area and perimeter, leading to incorrect calculations.
It is important to note that the perimeter, calculated in linear units, is the total length of the triangle’s sides, while the area, in square units, represents the space inside the triangle.
Mistake 3
Assuming that every triangular base is isosceles or equilateral, which results in inaccurate calculations.
A scalene triangle has all sides of different lengths. Always be careful about the type of the triangle to ensure accurate calculations.
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 your triangle.
Mistake 5
Misunderstanding or misidentifying the side lengths that are given in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if possible, try to draw a triangle to accurately identify the side lengths.
Perimeter of Triangular Prism Examples
Problem 1
A triangular prism has a base with a perimeter of 48 inches and two sides measuring 17 inches each. 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 missing side of the base. 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 perimeter of 297 inches is reshaped into a triangular prism base, forming an equilateral triangle. Find the length of each side of the triangle by dividing the total length by 3.
99 inches
Explanation
Given that the perimeter of the wire is equal to the total length of an equilateral triangle base formed by reshaping the wire: Perimeter of an 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 whose sides are 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 triangular prism-shaped structure in her backyard. She measures the three sides of the triangular base as: Side A = 12 meters Side B = 9 meters Side C = 15 meters How much material should Annie buy to cover the edges of the triangular base?
Annie will need 36 meters of material to cover the edges of the base.
Explanation
The perimeter of a triangular base is the sum of all the three sides. Using the formula: P = a + b + c P = 12 + 9 + 15 = 36 meters.
Problem 5
Find the perimeter of the scalene triangular base of a prism with sides a = 10, b = 8, c = 7.
Perimeter = a + b + c = 10 + 8 + 7 = 25 meters.
Explanation
Each side of the scalene triangle has a different length. The entire distance is calculated around the base to be 25 meters by summing the lengths of the three sides.
FAQs on Perimeter of Triangular Prism
1.Evaluate the perimeter of a triangular base if its sides are 3 cm, 4 cm, and 6 cm.
2.What is meant by the perimeter of a triangular prism’s base?
3.What are the types of triangles that can form the base of a prism?
4.Which triangle has no equal sides?
5.Which triangle has all sides equal?
Important Glossaries for Perimeter of Triangular Prism
Perimeter: The total length of the sides of a shape. Triangular Prism: A three-dimensional shape with two triangular bases and three rectangular faces. Equilateral Triangle: A triangle with all three sides of equal length. Scalene Triangle: A triangle with all sides of different lengths. Base: The face of a three-dimensional shape used as a reference for calculating perimeter or area.
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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
