A square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely. If a side of the first square is 4 cm, determine the sum of the areas all the square.

Answer: Option A

Side of the first square is 4 cm.
side of second square = $$2\sqrt{2}$$ cm.
Side of third square = 2 cm.
and so on, i.e. 4, 2, $$\sqrt{2}$$ , $$\sqrt{2}$$ , 1 ........
Thus, area of these square will be = 16, 8, 4, 2, 1, $$\frac{1}{2}$$ ..........
Hence, Sum of the area of first, second, third square
$$\begin{array}{rl}& =16+8+4+2+1+......\\ & =\frac{16}{1-\frac{1}{2}}\\ & =32c{m}^2\end{array}$$