What is the area of ​​the square formed by repeatedly connecting midpoints in a C program?

Suppose we have a square with side length "a". We will make more squares by repeatedly connecting the midpoints of the squares. The number of repetitions is n times. We have to find the area of ​​the nth square.

Since the side length of the outer square is "a", the area is

Now use Pythagoras According to Sri Lanka's theorem, we can get that the area of ​​the second rectangle is -

Similarly, the area of ​​the third ^rd square is -

Using this we can know that the area of ​​the nth square is-

Example

#include <iostream>
#include <cmath>
using namespace std;
float area(float a, float n) {
   if (a < 0 ) //if the value is negative it is invalid
      return -1;
   float area = (a*a) / pow(2, n-1);
   return area;
}
int main() {
   float a = 20.0, n = 10.0;
   cout << "Area : " << area(a, n);
}

Output

Area : 0.78125

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