Recursion squares

In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 22 cm.

Calculate:
a) the sum of perimeters of all squares
b) the sum of area of all squares

Correct result:

Σ p =  300.45 cm
Σ S =  968 cm2

Solution:

p1=422 qp=12 Σp=4221112=300.45 cm
 S1=222 qS=12 ΣS=2221112=968 cm2



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