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Octacontagon
If the polygon has n sides, it has n*(n - 3)/2 diagonals So, n(n - 3)/2 = 40 or n(n - 3)= 80 for which there is no solution. The question has no answer in terms of plane geometry.
80-5= 75
When the given vertices are plotted and joined together on the Cartesian plane they will form a 4 sided quadrilateral whose diagonals intercept each other at right angles and so multiplying the lengths of the diagonals divided by two will produce an area of 80 square units.
It depends on the shape of the area. It could be a perfect square or a sknny rectangle. The length would be affected by the shape.