A square is drawn by joining the mid-points of the sides of a given square. A third square is drawn inside the second square in the same way & this process continues indefinitely. If a side of the first square is 4 cm, then the sum of the areas of all the square is:

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Solution

The correct option is B 32
Side of big square is $4$
side of next square is $\sqrt{2^{2} + 2^{2}} = 2 \sqrt{2}$ and so on
Sum of area of squares is $4^{2} + (2 \sqrt{2})^{2} + (2)^{2} + (\sqrt{2})^{2} + \dots = \frac{16}{1 - \frac{1}{2}} = 32$

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A square is drawn by joining the mid-points of the sides of a given square. A third square is drawn inside the second square in the same way & this process continues indefinitely. If a side of the first square is 4 cm, then the sum of the areas of all the square is:

The correct option is B 32Side of big square is 4side of next square is √22+22=2√2 and so onSum of area of squares is 42+(2√2)2+(2)2+(√2)2+⋯=161−12=32

The correct option is B 32
Side of big square is $4$
side of next square is $\sqrt{2^{2} + 2^{2}} = 2 \sqrt{2}$ and so on
Sum of area of squares is $4^{2} + (2 \sqrt{2})^{2} + (2)^{2} + (\sqrt{2})^{2} + \dots = \frac{16}{1 - \frac{1}{2}} = 32$