A closed planar quadrilateral with opposite sides of equal lengths and ,
and with four right angles. A square is a degenerate rectangle with a=b
The area of the rectangle is A=ab
and its polygon diagonals p and q are of length
[latex]
p = q = \sqrt{(a{^2}+b{^2})}
[/latex]
A rectangle has a circumcircle with circumradius
[latex]
R = (1 \div 2) \sqrt{(a{^2}+b{^2})}
[/latex]
but incircle only in the degenerate case of a square.
Reference : http://mathworld.wolfram.com/Rectangle.html