Sorry, no such animal exists. The largest possible area for a rectangle with a given perimeter is when the rectangle is a square with sides that each measure one-fourth of the perimeter, or as in this case sides that measure times the measure of the diagonal. Hence the largest possible area for a rectangle with a diagonal of 4 is a square with sides that measure , and which therefore has an area of 8 square feet -- not anywhere near 20 square feet.
John
My calculator said it, I believe it, that settles it
