Problem C

A Square in a Square

In the diagram, \(PQRS\) is a square. Points \(T\), \(U\), \(V\), and \(W\) are on sides \(PQ\), \(QR\), \(RS\), and \(ST\), respectively, forming square \(TUVW\).

If \(PT=QU=RV=SW=4\) m and \(PQRS\) has area \(256\text{ m}^2\), determine the area of \(TUVW\).

**Theme(s):** Geometry, Number Sense