Answer: Option D.
Diagonal QS of square PQRS = √2 * a = √2 * 5 cm
Since ΔQST ΔUTS
OS = UT = 5√2, also QT = US
SR = RT = 5cm as R is the mid point given
QR = 5cm. and also ∠RQ = 90° as PQRS is a square.
So QRT=90° (By linear Pair).
In Rt. ΔQRT by Pythagoras
QT = 5√2 = US,
Similarly in Rt. ΔSRU, RU=5cm,
Now QSUT is a quadrilateral with all sides equal & diagonals ⊥ and equal, so QSUT is a square.
Area of QSUT = 5√2 * 5√2 = 50 cm2
Hence, option D.