# Sum of Area of all possible square inside a rectangle

• Difficulty Level : Medium
• Last Updated : 22 Jun, 2022

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 rectangle int 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 Code int main() {     int l = 4, b = 3;           cout<

## Java

 // Java program to calculate the // sum of area of all possible // squares that comes inside // the rectangle class GFG { // Function to calculate the // sum of area of all possible // squares that comes inside // the rectangle static 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 Code public 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 rectangle def 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 Code if __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 rectangle using System;   class GFG { // Function to calculate the // sum of area of all possible // squares that comes inside // the rectangle static 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 Code public static void Main() {     int l = 4, b = 3;           Console.Write(calculateAreaSum(l,b)); } }   // This code is contributed // by ChitraNayal



## Javascript



Output:

54

Time complexity: O(min(l,b))

space complexity: O(1)

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