Question 1012989
to find the area of the rectangle {{{PQRS}}} we need the length of the side

P,Q,R, and S are midpoints of  AB, BC, CD and AD respectively of square ABCD.
So, that the quadrilateral PQRS is {{{square}}} (special case of rectangle) inscribed in the square ABCD 

{{{drawing( 600, 600, -5, 5, -5,5,

circle(0,0,.1),circle(0,3,.1),circle(3,0,.1),circle(3,3,.1),
circle(1.5,0,.1),circle(0,1.5,.1),circle(3,1.5,.1),circle(1.5,3,.1),
line(3,0,3,3),line(0,3,3,3),
line(0,1.5,1.5,3),line(1.5,0,3,1.5),
line(1.5,3,3,1.5),line(0,1.5,1.5,0),
 graph( 600, 600, -5, 5, -5, 5, 0)) }}}


If the length of each side of the square ABCD is {{{3cm}}}, then the length of  the side  {{{PQRS}}} is {{{sqrt((3cm/2)^2+(3cm/2)^2)=sqrt(9cm^2/4+9cm^2/4)=sqrt(18cm^2/4)=sqrt(4.5cm^2)}}}

the area of the rectangle {{{PQRS}}} is:{{{A=(sqrt(4.5cm^2))^2=4.5cm}}}