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Infinitely many.

You can have a circle with a radius of approx 1.78 units.

Or, for any positive value of x,

an ellipse whose axes are x units and pi/(10*x) units in length,

a triangle whose base is x units and whose vertical height is 20/x units,

a parallelogram whose base is x units and whose vertical height is 10/x units.

And then there are polygons of 5, 6, sides and so on.

You can also combine a triangle with an area of 4 units with a semicircle with an area of 6 units and other weird and wonderful shapes.

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