Correct : c

The correct answer is Option C — 8 cm².
PQRS is a square with side 2 cm. PLMN is a rectangle where corner L lies on side QR, and side MN passes through corner S of the square.
Let PL = a (the length of the rectangle along PQ extended) and LM = b (the width). Since L is on QR and MN passes through S, using the geometric constraint that the rectangle''s diagonal or side must align with corner S, we can set up the relationship.
P is at origin (0,0), Q at (2,0), R at (2,2), S at (0,2). L is on QR so L = (2, h) for some h. N is on PS extended, so N = (0, h). M = (2+d, h) for some extension d, and MN passes through S=(0,2).
The line MN passes through S(0,2) and M. Since N=(0,h) and MN is horizontal (rectangle), MN passes through S means h=2. So L=(2,2)=R, which means PL = PQ extended to R, giving PL = 2√2 (diagonal of square) and LM = 2√2.
Area = PL × LM = 2√2 × 2√2 = 8 cm².