Recursion squares

In the square, ABCD has inscribed a square so that its vertices lie at the centers of the sides of the square ABCD. The procedure of inscribing the square is repeated this way. The side length of the square ABCD is a = 16 cm.

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

Correct answer:

Σ p =  218.51 cm
Σ S =  512 cm2

Step-by-step explanation:

p1=416 qp=21 Σp=4161211=218.51 cm
 S1=162 qS=21 ΣS=1621211=512 cm2

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