# Total area of two overlapping rectangles

Given two overlapping rectangles on a plane. We are given bottom left and top right points of the two rectangles. We need to find the total area (Green and pink areas in the below diagram). Examples:

```Input : Point l1 = {2, 2}, r1 = {5, 7};
Point l2 = {3, 4}, r2 = {6, 9};
Output :Total Area = 24

Input : Point l1 = {2, 1}, r1 = {5, 5};
Point l2 = {3, 2}, r2 = {5, 7};
Output :Total Area = 16
```

We basically add areas of two rectangles. This includes the intersecting part twice, so we subtract the area of intersecting part.

```Total Area = (Area of 1st rectangle +
Area of 2nd rectangle) -
Area of Intersecting part
```

Area of Rectangle = x_distance * y_distance

Where,
x_distance for 1st rectangle = abs(l1.x – r1.x)
y_distance for 1st rectangle = abs(l1.y – r1.y)

Similarly, we can compute area of 2nd rectangle.

For area of intersecting part,
x_distance for intersecting rectangle = min(r1.x, r2.x) – max(l1.x, l2.x)
y_distance for 1st rectangle = min(r1.y, r2.y) – max(l1.y, l2.y)

Below is the implementation of the above approach:

## C++

 `// C++ program to find total area of two` `// overlapping Rectangles` `#include ` `using` `namespace` `std;`   `struct` `Point {` `    ``int` `x, y;` `};`   `// Returns Total Area  of two overlap` `// rectangles` `int` `overlappingArea(Point l1, Point r1, Point l2, Point r2)` `{` `    ``// Area of 1st Rectangle` `    ``int` `area1 = ``abs``(l1.x - r1.x) * ``abs``(l1.y - r1.y);`   `    ``// Area of 2nd Rectangle` `    ``int` `area2 = ``abs``(l2.x - r2.x) * ``abs``(l2.y - r2.y);`   `    ``// Length of intersecting part i.e` `    ``// start from max(l1.x, l2.x) of` `    ``// x-coordinate and end at min(r1.x,` `    ``// r2.x) x-coordinate by subtracting` `    ``// start from end we get required` `    ``// lengths` `    ``int` `areaI = (min(r1.x, r2.x) - max(l1.x, l2.x))` `                ``* (min(r1.y, r2.y) - max(l1.y, l2.y));`   `    ``return` `(area1 + area2 - areaI);` `}`   `// Driver's Code` `int` `main()` `{` `    ``Point l1 = { 2, 2 }, r1 = { 5, 7 };` `    ``Point l2 = { 3, 4 }, r2 = { 6, 9 };` `  `  `    ``// Function Call` `    ``cout << overlappingArea(l1, r1, l2, r2);` `    ``return` `0;` `}`

## Java

 `// Java program to find total area of two` `// overlapping Rectangles` `class` `GFG {`   `    ``static` `class` `Point {` `        ``int` `x, y;`   `        ``public` `Point(``int` `x, ``int` `y)` `        ``{` `            ``this``.x = x;` `            ``this``.y = y;` `        ``}` `    ``};`   `    ``// Returns Total Area of two overlap` `    ``// rectangles` `    ``static` `int` `overlappingArea(Point l1, Point r1, Point l2,` `                               ``Point r2)` `    ``{` `        ``// Area of 1st Rectangle` `        ``int` `area1` `            ``= Math.abs(l1.x - r1.x) * Math.abs(l1.y - r1.y);`   `        ``// Area of 2nd Rectangle` `        ``int` `area2` `            ``= Math.abs(l2.x - r2.x) * Math.abs(l2.y - r2.y);`   `        ``// Length of intersecting part i.e` `        ``// start from max(l1.x, l2.x) of` `        ``// x-coordinate and end at min(r1.x,` `        ``// r2.x) x-coordinate by subtracting` `        ``// start from end we get required` `        ``// lengths` `        ``int` `areaI` `            ``= (Math.min(r1.x, r2.x) - Math.max(l1.x, l2.x))` `              ``* (Math.min(r1.y, r2.y)` `                 ``- Math.max(l1.y, l2.y));`   `        ``return` `(area1 + area2 - areaI);` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``Point l1 = ``new` `Point(``2``, ``2``), r1 = ``new` `Point(``5``, ``7``);` `        ``Point l2 = ``new` `Point(``3``, ``4``), r2 = ``new` `Point(``6``, ``9``);` `      `  `        ``// Function Call` `        ``System.out.println(overlappingArea(l1, r1, l2, r2));` `    ``}` `}`   `// This code is contributed by PrinciRaj1992`

## Python3

 `# Python program to find total area of two` `# overlapping Rectangles` `# Returns Total Area  of two overlap` `#  rectangles`   `def` `overlappingArea(l1, r1, l2, r2):` `    ``x ``=` `0` `    ``y ``=` `1` `    `  `    ``# Area of 1st Rectangle` `    ``area1 ``=` `abs``(l1[x] ``-` `r1[x]) ``*` `abs``(l1[y] ``-` `r1[y])`   `    ``# Area of 2nd Rectangle` `    ``area2 ``=` `abs``(l2[x] ``-` `r2[x]) ``*` `abs``(l2[y] ``-` `r2[y])`   `    ``''' Length of intersecting part i.e  ` `        ``start from max(l1[x], l2[x]) of  ` `        ``x-coordinate and end at min(r1[x], ` `        ``r2[x]) x-coordinate by subtracting  ` `        ``start from end we get required  ` `        ``lengths '''` `    ``areaI ``=` `((``min``(r1[x], r2[x]) ``-` `              ``max``(l1[x], l2[x])) ``*` `             ``(``min``(r1[y], r2[y]) ``-` `                 ``max``(l1[y], l2[y])))`   `    ``return` `(area1 ``+` `area2 ``-` `areaI)`     `# Driver's Code` `l1 ``=` `[``2``, ``2``]` `r1 ``=` `[``5``, ``7``]` `l2 ``=` `[``3``, ``4``]` `r2 ``=` `[``6``, ``9``]`   `# Function call` `print``(overlappingArea(l1, r1, l2, r2))`   `# This code is contributed by Manisha_Ediga`

## C#

 `// C# program to find total area of two` `// overlapping Rectangles` `using` `System;`   `class` `GFG {` `    ``public` `class` `Point {` `        ``public` `int` `x, y;`   `        ``public` `Point(``int` `x, ``int` `y)` `        ``{` `            ``this``.x = x;` `            ``this``.y = y;` `        ``}` `    ``};`   `    ``// Returns Total Area of two overlap` `    ``// rectangles` `    ``static` `int` `overlappingArea(Point l1, Point r1, Point l2,` `                               ``Point r2)` `    ``{` `        ``// Area of 1st Rectangle` `        ``int` `area1` `            ``= Math.Abs(l1.x - r1.x) * Math.Abs(l1.y - r1.y);`   `        ``// Area of 2nd Rectangle` `        ``int` `area2` `            ``= Math.Abs(l2.x - r2.x) * Math.Abs(l2.y - r2.y);`   `        ``// Length of intersecting part i.e` `        ``// start from max(l1.x, l2.x) of` `        ``// x-coordinate and end at min(r1.x,` `        ``// r2.x) x-coordinate by subtracting` `        ``// start from end we get required` `        ``// lengths` `        ``int` `areaI` `            ``= (Math.Min(r1.x, r2.x) - Math.Max(l1.x, l2.x))` `              ``* (Math.Min(r1.y, r2.y)` `                 ``- Math.Max(l1.y, l2.y));`   `        ``return` `(area1 + area2 - areaI);` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `Main(String[] args)` `    ``{` `        ``Point l1 = ``new` `Point(2, 2), r1 = ``new` `Point(5, 7);` `        ``Point l2 = ``new` `Point(3, 4), r2 = ``new` `Point(6, 9);` `      `  `        ``// Function Call` `        ``Console.WriteLine(overlappingArea(l1, r1, l2, r2));` `    ``}` `}`   `// This code is contributed by PrinciRaj1992`

Output

```24

```

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.