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Area of a square is equal to the product of sides of the square.

We are considering a figure in which the midpoints of sides of each square make another square. And so on until a specific number of squares.

This figure shows a square made by joining the midpoints of a square.

For this figure the let the side be a,

The length of side of inner square will be

L2 = (a/2)^{2}+ (a/2)^{2}L2 = a^{2}(1/4 + 1/4) = a^{2}(1/2) = a^{2}/2 L = a^{2}/ (\sqrt{2}).

Area of square2 = L2 = a^{2}/2.

For the next square, the area of square 3 = a^{2}/4

Lets take an example, tge

Now are we can infer from here about areas of consecutive squares,

a^{2}, a^{2}/2, a^{2}/4, a^{2}/8, …..

This is a GP with a^{2} being the first term of the and ½ being the common ratio.

#include <stdio.h> #include <math.h> int main() { double L = 2, n = 10; double firstTerm = L * L; double ratio = 1 / 2.0; double are = firstTerm * (pow(ratio, 10)) ; printf("The area of %lfth square is %lf", n , sum); return 0; }

The area of 10th square is 0.003906

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