Question

A square is drawn by joining the mid points of the given square a third square in the same way andthis process continues indefinitely. If a side of the first square is 16 cm, then the sum of the areas ofall the squares 1) 128 sq. cm 2) 256 sq. cm 3) 512 sq. cm 4) 1024 sq. cm​

Answer 1

Answer:

side of 1st square is 16 cm then by joining it's midpoint we get an another square, and at the corner it made a right angle triangle whose legs are of (16/2) 8cm, so side of that (2nd)square is 8√2cm(by Pythagoras theorem). similarly side of 3rd square is 8cm, 4th is 4√2cm, 5th is 4cm, 6th is 2√2cm, 7th is 2 cm, 8th is √2 cm and 9th is 1cm. so total area= 16^2+8√2^2+8^2+4√2^2+4^2+2√2^2+2^2+√2^2+1^2=511~512