Firstly , area of outermost square = (4)2 = 16
Then we need to find side length of next inner square..As it is given mid points are joined hence by Pythagoras theorem :
side = sqrt(22 + 22) = sqrt(8)
Hence area of next inner square = side * side = 8
Likewise area of next to next inner square will come out to be 4 and this will continue infinitely..Hence we get the series :
16 , 8 , 4 , 2 , ............... which is a decreasing G.P. with common ratio = 1/2 and initial term = 16..
We know ,
Sum of infinite G.P. = a / (1 - r) where |r| < 1 and hence a decreasing G.P.
= 16 / (1 - 1/2)
= 32
Hence total area = 32