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104 LearnersLast updated on September 17, 2025
Area of Oval
Area is the space inside the boundaries of a two-dimensional shape or surface. Different formulas are used to find the area of various shapes/figures. These formulas are widely used in architecture and design. In this section, we will find the area of an oval.
What is the Area of an Oval?
An oval is an elongated circle, commonly referred to as an ellipse.
It has two main axes: the major axis and the minor axis. The area of an oval is the total space it encloses.
Area of the Oval Formula
To find the area of an oval, we use the formula: π × a × b, where 'a' is the semi-major axis and 'b' is the semi-minor axis. Now let’s see how the formula is derived.
Derivation of the formula:- An oval is symmetrical about both its axes. The semi-major axis 'a' is half the length of the longest diameter, while the semi-minor axis 'b' is half the length of the shortest diameter.
The area of an ellipse is derived from its geometric properties, giving us the formula: Area = π × a × b Therefore, the area of the oval = π × a × b
How to Find the Area of an Oval?
We can find the area of an oval using the formula involving the semi-major and semi-minor axes. Here's how to use the formula:
Method Using the Semi-Major and Semi-Minor Axes
If the semi-major axis 'a' and semi-minor axis 'b' are given, we find the area of the oval using the formula: Area = π × a × b
For example, if 'a' and 'b' are 5 cm and 3 cm, the area of the oval will be: Area = π × a × b = π × 5 × 3 = 15π The area of the oval is approximately 47.12 cm² (using π ≈ 3.14).
Unit of Area of Oval
We measure the area of an oval in square units. The measurement depends on the system used:
In the metric system, the area is measured in square meters (m²), square centimeters (cm²), and square millimeters (mm²).
In the imperial system, the area is measured in square inches (in²), square feet (ft²), and square yards (yd²).
Special Cases or Variations for the Area of Oval
Ovals can vary, but the most common is the ellipse. Here are some special cases:
Case 1: Use of Semi-Major and Semi-Minor Axes If 'a' and 'b' are given, use the formula: Area = π × a × b
Case 2: Using Trigonometry for Elliptical Segments If only segments of the ellipse are considered, trigonometric functions may be used to calculate the area of those segments.
Tips and Tricks for Area of Oval
To ensure accurate results while calculating the area of an oval, consider these tips and tricks:
1. Ensure you correctly identify the semi-major and semi-minor axes.
2. Use the value of π accurately (3.14 or more decimal places for more precision).
3. Always check the units of measurement and convert if necessary to maintain consistency.
Common Mistakes and How to Avoid Them in Area of Oval
It is common for people to make mistakes while finding the area of an oval. Let’s take a look at some mistakes made:
Mistake 1
Confusing the semi-major and semi-minor axes
Ensure that you correctly identify 'a' as the semi-major axis and 'b' as the semi-minor axis, as reversing them will lead to incorrect calculations.
Mistake 2
Measuring the area using the wrong units
For the area to be in square meters (m²), both 'a' and 'b' should be in meters.
If one is in cm and the other is in m, convert the cm to m and find the area.
Mistake 3
Using approximations incorrectly
When using π, ensure that the level of precision is appropriate for the context, especially if high precision is required.
Area of Oval Examples
Problem 1
The semi-major axis 'a' and semi-minor axis 'b' of an oval-shaped garden are given as 7 m and 4 m. What will be the area?
We will find the area as 28π m²
Explanation
Here, the semi-major axis 'a' is 7 m and the semi-minor axis 'b' is 4 m.
The area of the oval = π × a × b = π × 7 × 4 = 28π m².
The approximate area is 87.92 m² (using π ≈ 3.14).
Problem 2
What will be the area of the oval if the semi-major and semi-minor axes are given as 10 cm and 6 cm?
We will find the area as 60π cm²
Explanation
If the semi-major axis 'a' and semi-minor axis 'b' are given, we use the formula: area = π × a × b.
Here, 'a' and 'b' are 10 cm and 6 cm.
Hence, the area will be π × 10 × 6 = 60π cm².
The approximate area is 188.4 cm² (using π ≈ 3.14).
Problem 3
The area of an oval is 150π m², and the length of the semi-major axis 'a' is 10 m.
We find the length of the semi-minor axis 'b' as 15 m.
Explanation
To find the semi-minor axis 'b', we use the formula: area = π × a × b.
Here, the area is 150π m², and 'a' is 10 m.
By substituting the values given, we find 'b': 150π = π × 10 × b 150 = 10 × b b = 150/10 = 15 m
FAQs on Area of Oval
1.Is it possible for the area of an oval to be negative?
2.How to find the area of an oval if the axes are given?
3.How to find the area of an oval segment?
4.How is the perimeter of the oval calculated?
5.What is meant by the area of an oval?
Glossaries of Terms Related to Area of Oval
- Area: The total space occupied by a shape. It tells us how much surface a shape covers.
- Oval: A geometrical shape that resembles a stretched circle, commonly known as an ellipse.
- Semi-Major Axis: The longest radius of an ellipse, half the length of the longest diameter.
- Semi-Minor Axis: The shortest radius of an ellipse, half the length of the shortest diameter.
- Ellipse: A regular oval shape, defined by its semi-major and semi-minor axes.
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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
