Given a square of side 20 in. The midpoints of its sides joined to form an inscribed square. The midpoints of this second square are joined to form a...

Given a square of side 20 in. The midpoints of its sides joined to form an inscribed square. The midpoints of this second square are joined to form a third square. If the process is continued endlessly, find the sum of the perimeters and the sum of the areas of all the squares, including the initial one.