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# Sum of Area of all possible square inside a rectangle

Given two integers L and B denoting the length and breadth of a rectangle respectively. The task is to calculate the sum of the area of all possible squares that comes into the rectangle.

Examples

Input: L = 4, B = 3
Output: 54

Input:  L = 2, B = 5
Output: 26

The idea is to observe the count of number of squares in a rectangle.

Now, the number of squares of side 1 will be 12 as there will be two cases one as squares of 1-unit sides along the horizontal(3) and second case as squares of 1-unit sides along the vertical(4). That gives us 3*4 = 12 squares.

When the side is 2 units, one case will be as squares of side of 2 units along only one place horizontally and second case as two places vertically. So the number of squares = 6
So we can deduce that,
Number of squares of size 1*1 will be L*B
Number of squares of size 2*2 will be (L-1)(B-1)
Therefore, the number of squares with size will be:

Number of square of size K = (L-K+1)*(B-K+1)

Therefore, area of total number of squares of size K will be:

Area of total number of square of size K = (L-K+1)*(B-K+1)*K*K

Below is the implementation of above idea:

## C++

 // CPP program to calculate the sum of area// of all possible squares that comes// inside the rectangle #include using namespace std; // Function to calculate the sum of area// of all possible squares that comes// inside the rectangleint calculateAreaSum(int l, int b){    int size = 1;         // Square with max size possible    int maxSize = min(l,b);         int totalArea = 0;         for(int i=1; i <= maxSize; i++)    {          // calculate total square of a given size        int totalSquares = (l-size+1)*(b-size+1);                 // calculate area of squares of a        // particular size           int area = totalSquares*size*size;                 // total area           totalArea += area;                  // increment size           size++;    }         return totalArea;} // Driver Codeint main(){    int l = 4, b = 3;         cout<

## Java

 // Java program to calculate the// sum of area of all possible// squares that comes inside// the rectangleclass GFG{// Function to calculate the// sum of area of all possible// squares that comes inside// the rectanglestatic int calculateAreaSum(int l, int b){    int size = 1;     // Square with max size possible    int maxSize = Math.min(l, b);     int totalArea = 0;     for(int i = 1; i <= maxSize; i++)    {        // calculate total square        // of a given size        int totalSquares = (l - size + 1) *                           (b - size + 1);             // calculate area of squares        // of a particular size        int area = totalSquares *                      size * size;             // total area        totalArea += area;                 // increment size        size++;    }     return totalArea;} // Driver Codepublic static void main(String[] args){    int l = 4, b = 3;         System.out.println(calculateAreaSum(l, b));}} // This code is contributed// by ChitraNayal

## Python 3

 # Python 3 program to calculate# the sum of area of all possible# squares that comes inside# the rectangle # Function to calculate the# sum of area of all possible# squares that comes inside# the rectangledef calculateAreaSum(l, b):    size = 1         # Square with max size possible    maxSize = min(l, b)         totalArea = 0         for i in range(1, maxSize + 1 ):         # calculate total square        # of a given size        totalSquares = ((l - size + 1) *                        (b - size + 1))                 # calculate area of squares        # of a particular size        area = (totalSquares *                size * size)                 # total area        totalArea += area                 # increment size        size += 1             return totalArea # Driver Codeif __name__ == "__main__":    l = 4    b = 3         print(calculateAreaSum(l,b)) # This code is contributed# by ChitraNayal

## C#

 // C# program to calculate the// sum of area of all possible// squares that comes inside// the rectangleusing System; class GFG{// Function to calculate the// sum of area of all possible// squares that comes inside// the rectanglestatic int calculateAreaSum(int l,                            int b){    int size = 1;     // Square with max size possible    int maxSize = Math.Min(l, b);     int totalArea = 0;     for(int i = 1; i <= maxSize; i++)    {        // calculate total square        // of a given size        int totalSquares = (l - size + 1) *                           (b - size + 1);             // calculate area of squares        // of a particular size        int area = totalSquares *                   size * size;             // total area        totalArea += area;                 // increment size        size++;    }    return totalArea;} // Driver Codepublic static void Main(){    int l = 4, b = 3;         Console.Write(calculateAreaSum(l,b));}} // This code is contributed// by ChitraNayal



## Javascript



Output

54

Complexity Analysis:

• Time complexity: O(min(l,b))
• Auxiliary complexity: O(1)

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