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Last updated on August 5th, 2025

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Perimeter of Base

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The perimeter of a shape is the total length of its boundary. The sum of all sides is called the perimeter of a base. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a base.

Perimeter of Base for Australian Students
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What is the Perimeter of a Base?

The perimeter of a base is the total length of all its sides. By adding the length of all sides, we get the perimeter of the shape. The formula for the perimeter of a base depends on the shape of the base. For instance, if the base is a rectangle with sides a = 6 and b = 8, then its perimeter is P = 2(a + b) = 2(6 + 8) = 28. For a square with side length a = 10, the perimeter is P = 4a = 4 × 10 = 40.

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Formula for Perimeter of Base - P = sum of all side lengths.

Let’s consider another example of a rectangular base with side lengths a = 8 and b = 12. So, the perimeter of the base will be: P = 2(a + b) = 2(8 + 12) = 40.

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How to Calculate the Perimeter of Base

To find the perimeter of a base, apply the formula specific to its shape and sum all the sides. For instance, for a square base with side a = 6, Perimeter = 4a = 4 × 6 = 24 cm. Example Problem on Perimeter of Base - For finding the perimeter of a rectangular base, use the formula, P = 2(a + b). For example, let’s say, a = 5 cm and b = 4 cm. Now, the perimeter = 2 × (5 + 4) = 18 cm. Therefore, the perimeter of the base is 18 cm.

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Tips and Tricks for Perimeter of Base

Learning some tips and tricks makes it easier for children to calculate the perimeter of bases. Here are some tips and tricks given below: Always remember that a base's perimeter is simply the sum of its sides. For that, use the formula specific to its shape. Calculating the perimeter of a base starts by determining the length of each side using the distance formula if necessary. 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. They can be found by adding the lengths of the sides after they are calculated. To reduce confusion, arrange the indicated side lengths if you need the perimeter of a group of bases. After that, apply the formula to each base. To avoid mistakes when adding the perimeter, make sure the side lengths are precise and constant for common uses like gardening and architecture. If you are given the semi-perimeter, which is half the perimeter, you can multiply it by 2 to determine the full perimeter. Area-related calculations, like those using Heron’s formula, often use the semi-perimeter.

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Common Mistakes and How to Avoid Them in Perimeter of Base

Did you know that while working with the perimeter of a base, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:

Mistake 1

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Incorrectly using the formula for the wrong shape.

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Remember that different shapes have different formulas for their perimeters. Ensure that you are using the correct formula for the shape of your base.

Mistake 2

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Students may confuse the concepts of area and perimeter, leading to incorrect calculations.

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It is important to note that the perimeter, calculated in linear units, is the total length of the base’s sides, while the area, in square units, represents the space inside the base.

Mistake 3

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Assuming that every base is a specific shape, which results in inaccurate calculations.

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A base can be any polygon with any number of sides. Always be careful about the base’s shape to ensure accurate calculations.

Mistake 4

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Using the wrong values for the length of the sides, misreading a problem, or mislabeling the sides.

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Double-check the problem and ensure that you're using the correct lengths for your base.

Mistake 5

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Misunderstanding or misidentifying the side lengths that are given in a problem outline.

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Before starting the calculations, make sure that you understand the problem and, if it's possible, try to draw the base to accurately identify the side lengths.

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Perimeter of Base Examples

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Problem 1

A rectangular garden has a perimeter of 60 meters and its length is twice its width. Find the dimensions of the garden.

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Width = 10 meters, Length = 20 meters.

Explanation

Let the width be "w" meters. Then, length = 2w meters. Perimeter of rectangle = 2(length + width) 60 = 2(2w + w) 60 = 6w w = 10 Therefore, width = 10 meters and length = 20 meters.

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Problem 2

A wire with a perimeter of 300 inches is reshaped into a square base. Find the length of each side of the square.

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75 inches

Explanation

Given that the perimeter of the wire is reshaped into a square base, here is the solution: Perimeter of a square = 4 × a 300 = 4 × a 300 ÷ 4 = 75 a = 75 Therefore, the length of each side of the square is 75 inches.

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Problem 3

Find the perimeter of a square base whose side length is 15 cm.

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60 cm

Explanation

Perimeter of a square = 4 × side length P = 4 × 15 = 60 Therefore, the perimeter of the square is 60 cm.

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Problem 4

Lucas is designing a rectangular flower bed in his backyard. He measures the length as 14 meters and the width as 8 meters. How much fencing is required to go around the flower bed?

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Lucas will need 44 meters of fencing.

Explanation

The perimeter of a rectangle is the sum of all the sides. Using the formula: P = 2(length + width) P = 2(14 + 8) = 44 meters.

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Problem 5

Find the perimeter of a triangular base with sides a = 13, b = 12, and c = 5.

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Perimeter = a + b + c = 13 + 12 + 5 = 30 meters.

Explanation

Each side of the triangular base has a different length. The entire distance is calculated around the base to be 30 meters by summing the lengths of the three sides.

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FAQs on Perimeter of Base

1.Evaluate the perimeter of a rectangular base if its sides are 7 cm and 3 cm.

Perimeter of rectangle = 2(length + width), Hence P = 2(7 + 3) = 20 cm.

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2.What is meant by a base’s perimeter?

The total length around a base’s sides is its perimeter. In other words, the perimeter of a base is the total length of its sides.

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3.What are the types of polygons that can be bases?

There are multiple types of polygons: triangles, rectangles, squares, pentagons, hexagons, etc.

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4.Which polygon has no equal sides?

A scalene triangle is a polygon with no equal sides. All three sides of the scalene triangle are different.

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5.Which polygon has the smallest perimeter for a given area?

For a given area, a circle has the smallest perimeter. However, among polygons, an equilateral triangle has a relatively small perimeter.

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Important Glossaries for Perimeter of Base

Perimeter: The total length of the sides of a shape. Base: The bottom or supporting part of various shapes, typically used for calculations. Polygon: A plane figure with at least three straight sides and angles, and typically five or more. Formula for perimeter: The mathematical expression used to calculate the perimeter of a base. Scalene Triangle: A triangle with all sides of different lengths.

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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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Fun Fact

: She has songs for each table which helps her to remember the tables

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