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104 LearnersLast updated on September 8, 2025
Perimeter of Curved Shapes
The perimeter of a shape is the total length of its boundary. The perimeter for curved shapes involves calculating the boundary that is not straight. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of curved shapes.
What is the Perimeter of Curved Shapes?
The perimeter of curved shapes is the total length around the shape. Unlike polygons, where the perimeter is the sum of straight sides, curved shapes involve arcs or curves.
For instance, the perimeter of a circle is called the circumference, calculated using the formula C=2πr, where r is the radius of the circle.
If a shape is a semicircle with a radius of 5, its perimeter is the sum of the straight line (the diameter) and the curved part (half the circumference), calculated as P = πr + 2r = π(5) + 10.
Formula for Perimeter of Curved Shapes
Let’s consider an example of a semicircle with a radius, r = 7.
The perimeter of the semicircle will be: P = πr + 2r = π(7) + 14 = 7π + 14.
How to Calculate the Perimeter of Curved Shapes
To find the perimeter of curved shapes, apply the relevant formulas for each specific shape. For example, for a circle, use C=2πr.
For a given semicircle with a radius of 6, the perimeter is calculated as P = πr + 2r = π(6) + 12 = 6π + 12 cm. Example Problem on Perimeter of Curved Shapes -
For finding the perimeter of an ellipse, use the approximation formula P ≈ π(3(a + b) - √((3a + b)(a + 3b))).
For instance, if a=5 cm and b=3 cm, then: P ≈ π(3(5 + 3) - √((3*5 + 3)(5 + 3*3))) P ≈ π(24 - √(18*14))
Therefore, following the calculation, you will get the approximate perimeter.
Tips and Tricks for Perimeter of Curved Shapes
Learning some tips and tricks makes it easier to calculate the perimeter of curved shapes. Here are some tips and tricks given below:
Always remember to use the correct formula for the specific shape you are dealing with, such as C=2πr for circles.
For shapes combining straight and curved edges, sum the lengths of all boundary parts. For example, the perimeter of a semicircle includes both the curved part and the diameter. When using approximations, especially for ellipses, be aware that they provide an estimate rather than an exact measure.
Ensure that measurements for radii and diameters are as precise as possible for accurate perimeter calculations.
In real-world applications, like designing tracks or garden paths, accounting for both the curved and straight portions of the boundary is crucial.
Common Mistakes and How to Avoid Them in Perimeter of Curved Shapes
Did you know that while working with the perimeter of curved shapes, people might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Misapplying formulas meant for polygons to curved shapes.
Ensure you use formulas specific to curved shapes, such as the circumference formula for circles, rather than using polygon formulas.
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 a shape’s boundary, while the area, in square units, represents the space inside the shape.
Mistake 3
Assuming all curves are part of circles, resulting in inaccurate calculations.
Different curved shapes like ellipses or arcs require specific formulas and approaches. Verify the shape type before calculating.
Mistake 4
Using the wrong values for radius or diameter, leading to errors in calculations.
Double-check the problem and ensure that you're using the correct measurements for your curved shape.
Mistake 5
Misunderstanding or misidentifying the given dimensions in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if possible, try to sketch the shape to accurately identify the necessary dimensions.
Perimeter of Curved Shapes Examples
Problem 1
A circular garden has a circumference of 44 meters. If a portion of the garden is fenced along a semicircular path, what length of fencing is needed?
Length of fencing needed = 22 + 14 ≈ 36 meters.
Explanation
The circumference of the circle is 44 meters, which gives us a diameter of 44/π.
For a semicircle, the perimeter includes half the circumference and the diameter: P = 22 + (44/2) = 22 + 22 = 44 meters.
Thus, the length of fencing needed is approximately 36 meters.
Problem 2
A racetrack is shaped like an ellipse with semi-major axis a = 150 meters and semi-minor axis b = 100 meters. Estimate the perimeter of the track using the approximation formula.
Approximately 785 meters.
Explanation
Using the approximation for an ellipse:
P ≈ π(3(a + b) - √((3a + b)(a + 3b))) P ≈ π(3(150 + 100) - √((3*150 + 100)(150 + 3*100))) P ≈ π(750 - √(550*450))
Calculate the above to get an estimated perimeter of approximately 785 meters.
Problem 3
Find the circumference of a circle with a radius of 10 cm.
62.8 cm
Explanation
Circumference of a circle = 2πr C = 2 * π * 10 ≈ 62.8 cm
Therefore, the circumference of the circle is approximately 62.8 cm.
Problem 4
A bridge arch is semicircular with a radius of 8 meters. Calculate the total length of the arch, including the base.
Annie will need 40.28 meters to go around the arch.
Explanation
The perimeter of the semicircle includes the arc and the diameter. Using the formula: P = πr + 2r P = π(8) + 16 ≈ 40.28 meters.
Problem 5
Calculate the perimeter of a sector with a radius of 6 cm and a central angle of 90 degrees.
Approximately 18.85 cm.
Explanation
The perimeter of a sector includes the arc length and the two radii.
Arc length = (θ/360) * 2πr P = (90/360) * 2π(6) + 2(6) ≈ 9.42 + 12 ≈ 18.85 cm.
FAQs on Perimeter of Curved Shapes
1.Evaluate the circumference of a circle if its radius is 3 cm.
2.What is meant by a curved shape’s perimeter?
3.What are the types of curved shapes?
4.Which shape has a perimeter equal to its circumference?
5.How do you find the perimeter of a sector?
Important Glossaries for Perimeter of Curved Shapes
- Perimeter: The total length of the boundary of a shape.
- Circumference: The perimeter of a circle or the total length around a circle.
- Arc: A portion of the circumference of a circle.
- Ellipse: An elongated circle or oval shape with a distinct perimeter calculation.
- Sector: A portion of a circle, bordered by two radii and an arc.
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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
