Area of an Ellipse
(KS3, Year 7)

The Lesson

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:

How to Find the Area of an Ellipse

Finding the area of an ellipse is easy.

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-by-Step:

1

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

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

Answer:

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.

"Find the Area" Widget

Here is a widget to help you learn the formulas to find the areas of different shapes.

Lesson Slides

The slider below shows another real example of how to find the area of an ellipse. Open the slider in a new tab

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.

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See Also

What is an ellipse?