Question

a square is drawn by joining the midpoints of the sides of a square of side 4cm. A third square is drawn inside the second square in the same way and this process continued indefinitely. determine the sum of areas of all the squares

Answer 1

see attachment ..................
hope it helps u

908e9ac19e669d9a2d520dcd5868f753.txt

Answer 2

this question is based on progression
now we proceed
at first time area of square=(4)^2=16
second area of square=(2root2)^2=8
third area of square =(2)^2=4
4th area of square=(root2)^2=2

now I think you understand series
i.e
16+8+4+2.........infinity

this is geometric progression
so use sum of Gp for infinity=a/(1-r)
actually here first term is 16
and r=1/2
so , sum =16/(1-1/2)
=32