Area of an Ellipse
(KS3, Year 7)
The LessonThe 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 EllipseFinding the area of an ellipse is easy.
QuestionWhat 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?
Start with the formula:
Area = πabDon't forget: π is pi (≈ 3.14) and πab = π × a × b
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
- Click on the shape you're learning about.
- Click on the pad to start.
- Follow the instructions in the bottom-left corner.
- On the last click, the formula, workings, and answer will appear in the yellow box.
- Good luck!
Lesson SlidesThe 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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