Area of squares formed by joining mid points repeatedly in C Program?
Suppose we have one square whose side is ‘a’. We will make more squares by attaching the mid-points of the squares repeatedly. The number of repetition is n times. We have to find the area of nth square.
![](https://www.tutorialspoint.com/assets/questions/media/27036/171.jpg)
As the side of the outer square is ‘a’, then area is
![](https://www.tutorialspoint.com/assets/questions/media/27036/171_1.jpg)
Now using Pythagorean theorem, we can get the area of the second rectangle is −
![](https://www.tutorialspoint.com/assets/questions/media/27036/171_2.jpg)
Similarly, area of 3rd square is −
![](https://www.tutorialspoint.com/assets/questions/media/27036/171_3.jpg)
Using this we can understand that the area of nth square is −
![](https://www.tutorialspoint.com/assets/questions/media/27036/171_4.jpg)
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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