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An ellipse is a two dimensional shape, so it does not have a "surface area", only an "area".

Any ellipse has two radii, the major one and the minor one. We'll call them R1 and R2. The area of the ellipse then can be calculated with the function:

a = πR1R2

You will notice that this is the same equation as the area for a circle. The circle is a special case though, because it is an ellipse in which both axes are the same length. In that case, R1 equals R2, so we can simply call it r and say:

a = πr2

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Q: How do you find the surface area of an ellipse?
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