104 LearnersLast updated on August 5th, 2025
Perimeter of Compound Shapes
The perimeter of a shape is the total length of its boundary. When dealing with compound shapes, the perimeter is the sum of the outer sides of all the simple shapes that form it. Perimeter is often used for tasks such as fencing a property, sewing, and more. In this topic, we will learn about the perimeter of compound shapes.
What is the Perimeter of a Compound Shape?
The perimeter of a compound shape is the total length of its outer sides. By adding the length of all the outer sides, we get the perimeter of the shape. For instance, consider a compound shape formed by a rectangle and a semicircle. If the rectangle has a length of 8 cm and a width of 4 cm, and the semicircle has a diameter of 4 cm, the perimeter is the sum of the rectangle's perimeter (excluding the side adjacent to the semicircle) and the semicircle's curved edge. Calculate the perimeter as follows: 8 + 4 + 4 + (π × 2) = 20 + 6.28 = 26.28 cm.
Formula for Perimeter of Compound Shapes
A compound shape can be broken down into simpler shapes. The perimeter is the sum of the outer sides of these shapes. For example, consider a compound shape formed by a rectangle and a triangle. If the rectangle's sides are 6 cm and 4 cm, and the triangle's sides are 3 cm, 4 cm, and 5 cm (only include the sides not shared with the rectangle), the perimeter is: P = 6 + 4 + 3 + 5 = 18 cm.
How to Calculate the Perimeter of Compound Shapes
To find the perimeter of a compound shape, identify the outer sides and sum their lengths. For instance, a compound shape is made of a square with a side of 5 cm and a semicircle with a diameter of 5 cm. The perimeter is the sum of three sides of the square and the semicircle's curved edge: Perimeter = 5 + 5 + 5 + (π × 2.5) = 15 + 7.85 = 22.85 cm. Example Problem on Perimeter of Compound Shape - For instance, if a compound shape consists of a rectangle with a length of 8 cm and width of 5 cm, and a semicircle with diameter 5 cm attached to one of the shorter sides, the perimeter is calculated as: P = 8 + 5 + π × 2.5 = 13 + 7.85 = 20.85 cm.
Tips and Tricks for Perimeter of Compound Shapes
Learning some tips and tricks makes it easier for children to calculate the perimeter of compound shapes. Here are some tips and tricks: Always identify and sum the length of the outer sides of the shape. Use the formula for each simple shape component, and add them together. When a compound shape includes a curved edge like a semicircle, calculate the curved perimeter separately and add it to the straight edges. To reduce confusion, arrange the indicated side lengths if you need the perimeter of a group of compound shapes. Apply the formula to each shape individually. For compound shapes that share sides between their components, ensure to count only the outer sides for the total perimeter. If you know the semi-perimeter of a component shape, you can use it in calculations for area-related problems but remember it’s not directly useful for perimeter calculations unless converting it to the full perimeter.
Common Mistakes and How to Avoid Them in Perimeter of Compound Shapes
Did you know that while working with the perimeter of compound shapes, children might encounter some errors or difficulties? Here are some solutions to resolve these problems:
Mistake 1
Ignoring shared sides between shapes in compound figures.
Always remember to count only the outer sides for the perimeter, ignoring any shared sides between component shapes.
Mistake 2
Confusing area calculations with perimeter calculations.
Perimeter is the total length around the shape, measured in linear units, while area is the space within the shape, measured in square units.
Mistake 3
Misjudging the length of curved edges.
For curved edges, such as semicircles, use the appropriate formula (e.g., π times the radius for a semicircle) to ensure accurate perimeter calculations.
Mistake 4
Overlooking the addition of all components in the compound shape.
Ensure all components of the shape are considered, and their perimeters are summed correctly.
Mistake 5
Using the wrong measurements or mislabeling dimensions.
Double-check the given measurements and ensure you’re using the correct values for each component of the shape.
Perimeter of Compound Shapes Examples
Problem 1
A garden is designed in the shape of a rectangle with a semicircle on one of its shorter sides. The rectangle is 10 m long and 4 m wide. Calculate the perimeter of the garden.
Perimeter of the garden is approximately 35.28 meters.
Explanation
The rectangle has a perimeter excluding the semicircle of 10 + 4 + 10 = 24 meters. The semicircle's curved edge is π × 2 = 6.28 meters. Thus, the total perimeter is 24 + 6.28 = 30.28 meters.
Problem 2
A running track is shaped like a rectangle with a semicircle at each end. The straight sides of the rectangle are 100 m, and the semicircle has a radius of 50 m. Calculate the perimeter of the track.
Approximately 471.4 meters
Explanation
The perimeter of the rectangle (excluding the semicircles) is 100 + 100 = 200 meters. Each semicircle has a curved length of π × 50 = 157.1 meters. Thus, the total perimeter is 200 + 157.1 = 471.4 meters.
Problem 3
Calculate the perimeter of a compound shape consisting of a rectangle 6 cm by 3 cm and a semicircle with a diameter of 3 cm on one of its shorter sides.
The perimeter is approximately 18.42 cm.
Explanation
The rectangle's perimeter excluding the semicircle is 6 + 3 + 6 = 15 cm. The semicircle's curved edge is π × 1.5 = 4.71 cm. Thus, the total perimeter is 15 + 4.71 = 19.71 cm.
Problem 4
A playground is in the shape of a rectangle with a semicircle on one of its longer sides. The rectangle is 20 m long and 10 m wide. Find the perimeter of the playground.
The perimeter of the playground is approximately 75.71 meters.
Explanation
The rectangle's perimeter excluding the semicircle is 20 + 10 + 20 = 50 meters. The semicircle's curved edge is π × 5 = 15.71 meters. Thus, the total perimeter is 50 + 15.71 = 75.71 meters.
Problem 5
Determine the perimeter of a compound shape made of a square with side 5 cm and a semicircle with diameter 5 cm attached to one side.
The perimeter is approximately 22.85 cm.
Explanation
The square's perimeter excluding the semicircle is 5 + 5 + 5 = 15 cm. The semicircle's curved edge is π × 2.5 = 7.85 cm. Thus, the total perimeter is 15 + 7.85 = 22.85 cm.
FAQs on Perimeter of Compound Shapes
1.Evaluate the perimeter of a compound shape formed by a rectangle 8 cm by 5 cm and a semicircle with diameter 5 cm.
2.What is meant by a compound shape’s perimeter?
3.What are the common components of compound shapes?
4.How do you calculate the perimeter of a shape with curved edges?
5.Can compound shapes include more than one type of simple shape?
Important Glossaries for Perimeter of Compound Shapes
Perimeter: The total length of the outer sides of a shape. Compound Shape: A shape composed of two or more simple shapes. Semicircle: A half-circle, forming part of a compound shape with a curved edge. Rectangle: A four-sided polygon with opposite sides equal in length. Curved Edge: The rounded portion of a shape, often present in semicircles.
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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
