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A square is drawn by joining mid-point of the sides of a square. Another square is drawn inside the second square in the same way and the process is continued indefinitely. If the side of the first square is 16 cm then what is the sum of the areas of all the squares?

Options

  1. A256 sq. cm
  2. B512 sq . cm
  3. C1024 sq. cm
  4. D512 / 3 sq. cm

Correct answer

B. 512 sq . cm

Step-by-step solution

Area of given square =256 ~cm ^2 Now length of square drawn by joining mid points =8 2 ~cm Area =128 ~cm ^2 Next area =64 ~cm ^2 And so on, Sum =256+128+64+32+ which is in G.P aligned & Sum = 256 1- 1 2 =256 2 & =512 sq. cm. aligned

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