# 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 cm

The area of the ellipse with a semi-minor axis of 3 cm and a semi-major axis of 5 cm is 47.1 cm^{2}^{2}.

# 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

##### Quick Test

**show**

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.