I am working on a project dealing with Kepler's laws. I have used MATLAB to plot sectoins from the foci of the ellipse to the outer rim. How can I find the complete areas of these sectors?

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The sectors come from one of the foci in the ellipse and look like triangles with one side being the curved outer rim of the ellipse.
I used "0.5*r^2*dtheta" to find the area of triangle I created out of the sector, but now I'd like to include the curve and find the exact areas.

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