The square ABCD has sides length 4cm. Point P is placed on somewhere on AB, but not actually at A or B. Point Q is placed on side BC so that BQ = AP. Point R is then placed on the perimeter of square ABCD so that triangle PQR is isosceles.

What is the minimum area of triangle PQR? What is the minimum perimeter for triangle PQR? Can you prove that your answer is correct?