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243 LearnersLast updated on August 5, 2025
Perimeter of Oval
The perimeter of a shape is the total length of its boundary. Calculating the perimeter of an oval, also known as an ellipse, is more complex than for a simple polygon. The perimeter is used in various applications like construction, design, and more. In this topic, we will learn about the perimeter of an oval.
What is the Perimeter of an Oval?
The perimeter of an oval, also called an ellipse, is the total length around its boundary. Unlike simple shapes, calculating the perimeter of an oval requires a more complex approach, as there is no exact formula like for polygons. However, an approximation formula for the perimeter of an oval is given by Ramanujanโs first approximation: ๐ท โ ฯ * [3(a+b) - โ((3a + b) * (a + 3b))], where a and b are the semi-major and semi-minor axes of the oval, respectively. For example, if an oval has a semi-major axis a = 6 and a semi-minor axis b = 4, then its approximate perimeter is ๐ท โ ฯ * [3(6+4) - โ((3*6 + 4) * (6 + 3*4))].
Formula for Perimeter of Oval - ๐ท โ ฯ * [3(a+b) - โ((3a + b) * (a + 3b))].
Letโs consider another example of an oval with semi-major and semi-minor axes, ๐ = 8, ๐ = 6. So the approximate perimeter of the oval will be: ๐ท โ ฯ * [3(8+6) - โ((3*8 + 6) * (8 + 3*6))].
How to Calculate the Perimeter of an Oval
To find the perimeter of an oval, apply the approximation formula by Ramanujan and use the given lengths of the semi-major and semi-minor axes. For instance, a given oval has semi-major axis a = 7 and semi-minor axis b = 5. Perimeter โ ฯ * [3(7+5) - โ((3*7 + 5) * (7 + 3*5))]. Example Problem on Perimeter of Oval - For finding the approximate perimeter of an oval, we use the formula, ๐ท โ ฯ * [3(a+b) - โ((3a + b) * (a + 3b))]. For example, letโs say, a semi-major axis a = 9 cm, and a semi-minor axis b = 6 cm. Now, the approximate perimeter โ ฯ * [3(9+6) - โ((3*9 + 6) * (9 + 3*6))].
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Tips and Tricks for Perimeter of Oval
Learning some tips and tricks makes it easier to calculate the perimeter of ovals. Here are some tips and tricks given below: Always remember that the perimeter of an oval requires more complex calculations than simple polygons. Use the approximation formula, ๐ท โ ฯ * [3(a+b) - โ((3a + b) * (a + 3b))]. When calculating the perimeter of an oval, ensure that you identify the correct lengths for the semi-major and semi-minor axes. This can be done by measuring the longest and shortest diameters of the oval and halving them. To reduce confusion, arrange your calculations systematically and verify your steps when determining the perimeter of a group of ovals. To avoid mistakes when calculating the perimeter, ensure the semi-major and semi-minor axes are precise and constant for practical uses like design and architecture. If you are given an estimated perimeter, verify the calculation by comparing it with different approximation methods or numerical integration techniques for more accuracy.
Common Mistakes and How to Avoid Them in Perimeter of Oval
Did you know that while working with the perimeter of an oval, people might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Incorrectly using a simple perimeter formula meant for polygons.
Remember that ovals require specific approximation methods, like Ramanujanโs formula, for calculating the perimeter. Using polygon formulas will result in incorrect calculations.
Mistake 2
Confusing the semi-major and semi-minor axes, leading to errors.
It is important to correctly identify the semi-major and semi-minor axes. The semi-major axis is the longest radius, and the semi-minor axis is the shortest radius of the oval.
Mistake 3
Assuming an oval is a perfect circle, resulting in inaccurate calculations.
An oval differs from a circle, which has all equal radii. Always ensure you understand the shapeโs characteristics to ensure accurate calculations.
Mistake 4
Using incorrect values for the axes, misreading a problem, or mislabeling them.
Double-check the problem and ensure that you're using the correct axis lengths for your oval.
Mistake 5
Misunderstanding or misidentifying the axesโ lengths that are given in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if possible, try to sketch the oval to accurately identify the semi-major and semi-minor axes.
Perimeter of Oval Examples
Problem 1
An elliptical racetrack has a semi-major axis of 50 meters and a semi-minor axis of 30 meters. Find the approximate perimeter using Ramanujan's formula.
Approximate perimeter = 252.15 meters.
Explanation
Let a = 50 meters and b = 30 meters. Using Ramanujanโs approximation: ๐ท โ ฯ * [3(50+30) - โ((3*50 + 30) * (50 + 3*30))] ๐ท โ ฯ * [3(80) - โ((150 + 30) * (50 + 90))] ๐ท โ ฯ * [240 - โ(180 * 140)] ๐ท โ ฯ * [240 - โ25200] ๐ท โ ฯ * [240 - 158.74] ๐ท โ ฯ * 81.26 ๐ท โ 255.15 meters. Therefore, the approximate perimeter is 255.15 meters.
Problem 2
A garden in the shape of an oval has a semi-major axis of 15 meters and a semi-minor axis of 10 meters. Calculate the approximate perimeter.
Approximate perimeter = 79.07 meters.
Explanation
Given a = 15 meters and b = 10 meters. Using Ramanujanโs approximation: ๐ท โ ฯ * [3(15+10) - โ((3*15 + 10) * (15 + 3*10))] ๐ท โ ฯ * [3(25) - โ((45 + 10) * (15 + 30))] ๐ท โ ฯ * [75 - โ(55 * 45)] ๐ท โ ฯ * [75 - โ2475] ๐ท โ ฯ * [75 - 49.75] ๐ท โ ฯ * 25.25 ๐ท โ 79.35 meters. Therefore, the approximate perimeter is 79.35 meters.
Problem 3
Find the approximate perimeter of an oval with semi-major axis 20 cm and semi-minor axis 14 cm.
Approximate perimeter = 107.06 cm.
Explanation
Using Ramanujanโs approximation: ๐ท โ ฯ * [3(20+14) - โ((3*20 + 14) * (20 + 3*14))] ๐ท โ ฯ * [3(34) - โ((60 + 14) * (20 + 42))] ๐ท โ ฯ * [102 - โ(74 * 62)] ๐ท โ ฯ * [102 - โ4588] ๐ท โ ฯ * [102 - 67.73] ๐ท โ ฯ * 34.27 ๐ท โ 107.67 cm. Therefore, the approximate perimeter is 107.67 cm.
Problem 4
An art piece is in the shape of an oval with a semi-major axis of 25 inches and a semi-minor axis of 18 inches. How much material is needed to frame the piece?
Approximate perimeter = 135.47 inches.
Explanation
Using Ramanujanโs approximation: ๐ท โ ฯ * [3(25+18) - โ((3*25 + 18) * (25 + 3*18))] ๐ท โ ฯ * [3(43) - โ((75 + 18) * (25 + 54))] ๐ท โ ฯ * [129 - โ(93 * 79)] ๐ท โ ฯ * [129 - โ7347] ๐ท โ ฯ * [129 - 85.72] ๐ท โ ฯ * 43.28 ๐ท โ 136.05 inches. Therefore, the approximate perimeter is 136.05 inches.
Problem 5
An oval mirror has a semi-major axis of 12 cm and a semi-minor axis of 8 cm. Calculate the approximate length around the mirrorโs edge.
Approximate perimeter = 63.58 cm.
Explanation
Using Ramanujanโs approximation: ๐ท โ ฯ * [3(12+8) - โ((3*12 + 8) * (12 + 3*8))] ๐ท โ ฯ * [3(20) - โ((36 + 8) * (12 + 24))] ๐ท โ ฯ * [60 - โ(44 * 36)] ๐ท โ ฯ * [60 - โ1584] ๐ท โ ฯ * [60 - 39.8] ๐ท โ ฯ * 20.2 ๐ท โ 63.45 cm. Therefore, the approximate perimeter is 63.45 cm.
FAQs on Perimeter of Oval
1.Evaluate the ovalโs perimeter if its semi-major axis is 10 cm and semi-minor axis is 5 cm.
2.What is meant by an ovalโs perimeter?
3.What are the axes of an oval?
4.Which shape is an oval similar to but not the same as?
5.Can a perfect formula be used for the perimeter of an oval?
Important Glossaries for Perimeter of Oval
Perimeter: The total length of the boundary of a shape. Oval: A curved shape resembling an elongated circle, also known as an ellipse. Semi-major axis: The longest radius of an oval. Semi-minor axis: The shortest radius of an oval. Ramanujanโs approximation: A formula used to estimate the perimeter of an oval.
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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