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Sum of Area of all possible square inside a rectangle
• Difficulty Level : Medium
• Last Updated : 04 Oct, 2018

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 `

## PHP

 ` `

Output:

```54
```

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