The area of an ellipse formula, leads on from how we work out the area of a circle.
If we think about the overall shape, an ellipse is usually fairly similar to a standard circle.
An ellipse often has the appearance of a stretched circle, or a compressed circle, depending on how we look at it.
Axis of an Ellipse
It’s the case that an ellipse is symmetrical in shape, on both a major axis and a minor axis.The major axis is the larger diameter, and the minor axis is the lesser diameter of an ellipse.
We can cut in half both the major and minor axis, which results in what is called the semi minor axis, and semi major axis.
Area of an Ellipse Formula
With a circle, the distance from the centre to any point of the outer edge is always the same value, this length is called the radius of the circle.
π × r2 or π × r × r
Area of Circle and Area of Ellipse
When we have an ellipse, the distance from the centre to the outer edge is not the same size all the way around like with a circle.But as we know, the overall shape of an ellipse is symmetrical.
With both of the semi major axis having the same length, and both of the semi minor axis also having the same length.
Thus in a similar way to how the area of a circle can be worked out by, π × r × r.
The area of an ellipse can be established by, π × a × b.
This is the area of an ellipse formula, that can be used to find the area of an ellipse.
Provided that you know the length of the semi minor axis and the semi major axis.
Examples
(1.1)
What is the area of the following ellipse.
Solution
Area = π × 12 × 5 = 188.50 ( to 2 decimal places )
The area of the ellipse is 188.50m2.
(1.2)
If the area of the following ellipse is 169.65m2.
Roughly what size is the length of the major axis?
Solution
169.65 = π × 6 × a ( ÷ π × 6 BOTH SIDES )
\frac{\bf{169.65}}{\pi \space \times \space {\bf{6}}} = a
9.0002… = a
The semi major axis a is roughly 9m in length.