125 LearnersLast updated on August 5th, 2025
Perimeter of Composite Figures
The perimeter of a shape is the total length of its boundary. In composite figures, the perimeter is the sum of the lengths of all outer sides. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about calculating the perimeter of composite figures.
What is the Perimeter of Composite Figures?
The perimeter of a composite figure is the total length of all its outer sides. By adding the length of these sides, we obtain the perimeter of the shape. For instance, if a composite figure consists of a rectangle and a semicircle with a rectangle's width of 4 cm and length of 8 cm, and a semicircle with a diameter of 4 cm, then its perimeter is calculated by adding the perimeter of the rectangle and the semicircle (half of the circle's circumference).
Formula for Perimeter of Composite Figures
Let’s consider an example of a composite figure comprising a square with a side of 5 cm and a semicircle on one side with a diameter of 5 cm. So the perimeter of the composite figure will be: Perimeter = Perimeter of the square + Perimeter of the semicircle = 4 × side + (π × diameter / 2) = 4 × 5 + (3.14 × 5 / 2) = 20 + 7.85 = 27.85 cm
How to Calculate the Perimeter of Composite Figures
To find the perimeter of a composite figure, we need to sum up the lengths of all the outside edges. For instance, consider a composite figure comprising a rectangle with dimensions 3 cm by 7 cm and a quarter circle with a radius of 3 cm. Perimeter = Perimeter of the rectangle + Perimeter of the quarter circle = 2 × (length + width) + (π × radius / 2) + radius = 2 × (3 + 7) + (3.14 × 3 / 2) + 3 = 20 + 4.71 + 3 = 27.71 cm
Tips and Tricks for Perimeter of Composite Figures
Learning some tips and tricks makes it easier to calculate the perimeter of composite figures. Here are some tips and tricks given below: Always remember that a composite figure's perimeter is the sum of the lengths of all its outer sides. Break the figure into simpler shapes and calculate each part separately. Calculating the perimeter of a composite figure starts by identifying the individual shapes and calculating their perimeters. Then sum these values for the total perimeter. To reduce confusion, specifically arrange the indicated side lengths before calculating the perimeter. Also, ensure you include only the outer boundaries. To avoid mistakes when calculating the perimeter, ensure the side lengths are precise and consistent for common uses like landscaping and construction. If a composite figure includes circular parts, remember to use the appropriate part of the circle's circumference in your calculations.
Common Mistakes and How to Avoid Them in Perimeter of Composite Figures
While working with the perimeter of composite figures, children might encounter some errors or difficulties. Here are some solutions to resolve these problems:
Mistake 1
Incorrectly assuming the perimeter of a composite figure is just the sum of all interior and exterior sides.
Remember, only the outer boundary lengths contribute to the perimeter. Be sure to include only those in your calculations.
Mistake 2
Confusing 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 figure’s outer sides, while the area, in square units, represents the space inside the figure.
Mistake 3
Assuming all components of a composite figure are regular, which results in inaccurate calculations.
Different shapes can make up a composite figure, and they may not all be regular. Always ensure correct identification and calculation of each component’s perimeter.
Mistake 4
Using incorrect values for the lengths of sides or misreading a problem.
Double-check the given dimensions and ensure you’re using the correct lengths for your calculations.
Mistake 5
Misunderstanding or misidentifying the parts of a composite figure.
Before starting the calculations, make sure that you understand the composition of the figure and, if possible, try to sketch it to accurately identify the parts.
Perimeter of Composite Figures Examples
Problem 1
A garden path is comprised of a rectangle and a semicircle. The rectangle is 10 meters long and 4 meters wide, and the semicircle is attached to one of the shorter sides. Calculate the perimeter of the path.
Perimeter of the path = 10 + 4 + 10 + (π × 4 / 2) = 38.28 meters
Explanation
Let's denote the longer side of the rectangle as L and the shorter side as W. Perimeter of the path = Length + Width + Length + Perimeter of semicircle = 10 + 4 + 10 + (3.14 × 4 / 2) = 24 + 6.28 = 30.28 meters.
Problem 2
A playground is shaped like a quarter circle with a radius of 7 meters, attached to a square of side 7 meters. Find the perimeter of the playground.
Perimeter of the playground = 21 + 10.99 = 31.99 meters
Explanation
Given that the playground consists of a square and a quarter circle, the solution is: Perimeter of the playground = Perimeter of the square + Perimeter of the quarter circle = 4 × side + (π × radius / 2) + radius = 4 × 7 + (3.14 × 7 / 2) + 7 = 28 + 10.99 + 7 = 45.99 meters.
Problem 3
Find the perimeter of a composite figure consisting of a triangle with sides 6 cm, 8 cm, and 10 cm, and a semicircle with a diameter of 8 cm attached to the longest side.
Perimeter of the composite figure = 6 + 8 + (3.14 × 8 / 2) = 28.56 cm
Explanation
Perimeter of the composite figure = Sum of triangle sides + Perimeter of semicircle = 6 + 8 + 10 + (3.14 × 8 / 2) = 24 + 12.56 = 36.56 cm.
Problem 4
A decorative piece is made by attaching a semicircle to a rectangle with a length of 15 cm and width of 6 cm. Calculate the perimeter of the decorative piece.
Perimeter of the decorative piece = 15 + 6 + 15 + (3.14 × 6 / 2) = 50.42 cm
Explanation
Perimeter of the decorative piece = 2 × Length + Width + Perimeter of semicircle = 15 + 6 + 15 + (3.14 × 6 / 2) = 36 + 9.42 = 45.42 cm.
Problem 5
Calculate the perimeter of a composite figure consisting of a rectangle 8 cm by 12 cm and a semicircle with a diameter equal to the rectangle's shorter side.
Perimeter of the composite figure = 16 + 12 + (π × 8 / 2) = 40.56 cm
Explanation
Perimeter of the composite figure = 2 × Length + Width + Perimeter of semicircle = 2 × 8 + 12 + (3.14 × 8 / 2) = 16 + 12 + 12.56 = 40.56 cm.
FAQs on Perimeter of Composite Figures
1.Evaluate the perimeter of a composite figure consisting of a rectangle 7 cm by 5 cm and a semicircle with a diameter of 5 cm.
2.What is meant by a composite figure's perimeter?
3.What are the types of shapes that can make up a composite figure?
4.How do you calculate the perimeter of a composite figure that includes circular components?
5.Can a composite figure have curved sides?
Important Glossaries for Perimeter of Composite Figures
Perimeter: The total length of the outer sides of a shape. Composite Figure: A shape made up of two or more simple shapes. Semicircle: Half of a circle. Circumference: The total length around a circle, calculated as π times the diameter. Rectangle: A quadrilateral with opposite sides equal and all angles right angles.
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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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: She has songs for each table which helps her to remember the tables
