A square is drawn by joining the mid points of 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 areas of all the squares.
A)20 cm² B)32 cm² C)64 cm² D)16 cm²

• B
  4^2 + 2*sqrt(2) + 2^2 + sqrt(2)^2 +......... = 16/ (1-1/2) = 32
• 3 years agoHelpfull: Yes(9) No(0)
• Side of big square is 4
  side of next square is
  2
  2
  +2
  2
  
  ​
  =2
  2
  ​
  and so on
  Sum of area of squares is 4
  2
  +(2
  2
  ​
  )
  2
  +(2)
  2
  +(
  2
  ​
  )
  2
  +⋯=
  1−
  2
  1
  ​
  
  16
  ​
  =32
• 3 years agoHelpfull: Yes(1) No(0)
• 16
  4+4+4+4
• 3 years agoHelpfull: Yes(0) No(3)
• =4^2 + (2*sqrt(2))^2 + 2^2 + sqrt(2)^2 + 1^2
  =16+8+4+2+1
  =31
• 3 years agoHelpfull: Yes(0) No(3)
• area of first square=16
  by pythagorus theorm take out the side of inner sqaure and thus the area
  so total area=16 + 8 + 4 +2 +1
• 3 years agoHelpfull: Yes(0) No(2)
• Area of 1st square = 4²
  2nd square = (2√2)²
  3rd square = 2²
  and so on......
  
  so, 4² + (2√2)² + 2² + ...... = 16 + 8 +4 + ...... = 16 / (1 - (1 / 2)) = 32 cm²
  
  Therefore the answer is option B
• 2 years agoHelpfull: Yes(0) No(0)