Diagram -
AP = PB = 2cm
∴ AB= = √8 = 2√2 cm
Similarly, BE = EH = 2√2/2 = √2 cm
∴ EH =
= √4 = 2 cm
If we write the infinite series of area of squares,
= 42 + (2√2)^{2} + 2^{2} + ……. infinite
Since it is a decreasing series sum of infinite terms can be approximated.
= 16+8+4+………infinite
∴ a (first term) = 16 , r = (in the infinite G.P)
Sum of an infinite G.P =
=
= 32 cm^{2}
Choice (C) is therefore, the correct answer.
Correct Answer: 32 cm^{2}