# 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 = 24Input :Point l1 = {2, 1}, r1 = {5, 5}; Point l2 = {3, 2}, r2 = {5, 7};Output :Total Area = 16

Asked in Juniper

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)

If the x_distance or y_distance is negative, then the two rectangles do not intersect. In that case, overlapping area is 0.

Below is the implementation of the above approach:

## C++

`// C++ program to find total area of two` `// overlapping Rectangles` `#include <bits/stdc++.h>` `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` `x_dist = min(r1.x, r2.x)` ` ` `- max(l1.x, l2.x);` ` ` `int` `y_dist = (min(r1.y, r2.y)` ` ` `- max(l1.y, l2.y));` ` ` `int` `areaI = 0;` ` ` `if` `( x_dist > 0 && y_dist > 0 )` ` ` `{` ` ` `areaI = x_dist * y_dist;` ` ` `}` ` ` ` ` `return` `(area1 + area2 - areaI);` `}` `// Driver 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` `x_dist = (Math.min(r1.x, r2.x)` ` ` `- Math.max(l1.x, l2.x);` ` ` `int` `y_dist = (Math.min(r1.y, r2.y)` ` ` `- Math.max(l1.y, l2.y);` ` ` `int` `areaI = ` `0` `;` ` ` `if` `( x_dist > ` `0` `&& y_dist > ` `0` `)` ` ` `{` ` ` `areaI = x_dist * y_dist;` ` ` `}` ` ` `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 '''` ` ` `x_dist ` `=` `(` `min` `(r1[x], r2[x]) ` `-` ` ` `max` `(l1[x], l2[x]))` ` ` `y_dist ` `=` `(` `min` `(r1[y], r2[y]) ` `-` ` ` `max` `(l1[y], l2[y]))` ` ` `areaI ` `=` `0` ` ` `if` `x_dist > ` `0` `and` `y_dist > ` `0` `:` ` ` `areaI ` `=` `x_dist ` `*` `y_dist` ` ` `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` `x_dist` ` ` `= (Math.Min(r1.x, r2.x) - Math.Max(l1.x, l2.x));` ` ` `int` `y_dist` ` ` `= (Math.Min(r1.y, r2.y) - Math.Max(l1.y, l2.y));` ` ` `int` `areaI = 0;` ` ` `if` `(x_dist > 0 && y_dist > 0) {` ` ` `areaI = x_dist * y_dist;` ` ` `}` ` ` `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` |

## Javascript

`<script>` `// Javascript program to find total area of two` `// overlapping Rectangles` `// Returns Total Area of two overlap` `// rectangles` ` ` ` ` `function` `overlappingArea(l1, r1, l2, r2)` `{` ` ` `let x = 0` ` ` `let y = 1` ` ` ` ` `// Area of 1st Rectangle` ` ` `let area1 = Math.abs(l1[x] - r1[x]) * Math.abs(l1[y] - r1[y])` ` ` ` ` `// Area of 2nd Rectangle` ` ` `let 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` ` ` `let x_dist = (Math.min(r1[x], r2[x]) -` ` ` `Math.max(l1[x], l2[x]))` ` ` ` ` `let y_dist = (Math.min(r1[y], r2[y]) -` ` ` `Math.max(l1[y], l2[y]))` ` ` `let areaI = 0` ` ` `if` `(x_dist > 0 && y_dist > 0)` ` ` `areaI = x_dist * y_dist` ` ` ` ` `return` `(area1 + area2 - areaI)` `}` ` ` `// Driver Code` ` ` ` ` `let l1 = [2, 2]` ` ` `let r1 = [5, 7]` ` ` `let l2 = [3, 4]` ` ` `let r2 = [6, 9]` ` ` `// Function call` ` ` `document.write(overlappingArea(l1, r1, l2, r2))` ` ` `// This code is contributed by jana_sayantan. ` ` ` `</script>` |

**Output**

24

Attention reader! Don’t stop learning now. Participate in the **Scholorship Test for First-Step-to-DSA Course for Class 9 to 12 students**.