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How to Find the Area of an Ellipse (Mathematics Lesson)

How to Find the Area of an Ellipse

The area of an ellipse is found using the formula:



In this formula, a is the semi-minor axis and b is the semi-major axis. The image below shows what we mean by the semi-minor and semi-major axis:

A Real Example of How to Find the Area of an Ellipse

An Example Question

What is the area of an ellipse with a semi-minor axis of 3 cm and a semi-major axis of 5 cm, as shown below?

Step 1
Start with the formula:
Area = πab
Don't forget: π is pi (≈ 3.14) and πab = π × a × b

Step 2
Substitute the semi-minor and semi-major axis into the formula. In our example, a = 3 and b = 5.
Area = π × 3 × 5 = 47.1 cm2
The area of the ellipse with a semi-minor axis of 3 cm and a semi-major axis of 5 cm is 47.1 cm2.

Another Real Example of How to Find the Area of an Ellipse

The slider below shows another real example of how to find the area of an ellipse:
Curriculum
Geometry Lessons
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Here's a second test on finding the area of an ellipse.
Here's a third test on finding the area of an ellipse.
Note

What Is An Ellipse?

An ellipse is a squashed circle.

It is symmetrical about its longest axis (called the major axis) and its shortest axis (called the minor axis).



Half of the major axis is the semi-major axis.

Half of the minor axis is the semi-minor axis.