Question

A square is drawn by joining the mid points of the sides of given square. A second square is drawn inside the second square in the same way Second Square is drawn inside the third square and this process continues upto 8th square. If a side of the first square is 32 cm then find the area of the first to eight square.​

Answer 1

Side of the square is 10cm

So, area of square =100cm  2

Now Area of second Square is =  2 1  × area  of  first  square=50cm  2

 Area of third square =25cm  2

 Clearly 100,50,25... a G.P

With first term (a)=100

and common ration (r)=  

So, Sum of all square = Sum of G.P to infinity = 1−r a  =  1−  2 1

​ 100  =200cm  2

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