# Program to find area of a triangle

• Difficulty Level : Easy
• Last Updated : 05 Aug, 2022

### Given the sides of a triangle, the task is to find the area of this triangle.

Examples :

Input : a = 5, b = 7, c = 8
Output : Area of a triangle is 17.320508

Input : a = 3, b = 4, c = 5
Output : Area of a triangle is 6.000000
Recommended Practice

Approach: The area of a triangle can simply be evaluated using following formula.

where a, b and c are lengths of sides of triangle, and
s = (a+b+c)/2

Below is the implementation of the above approach:

## C++

 // C++ Program to find the area  // of triangle  #include  using namespace std;   float findArea(float a, float b, float c)  {      // Length of sides must be positive      // and sum of any two sides      // must be smaller than third side.      if (a < 0 || b < 0 || c < 0 ||         (a + b <= c) || a + c <= b ||                         b + c <= a)      {          cout << "Not a valid triangle";          exit(0);      }      float s = (a + b + c) / 2;      return sqrt(s * (s - a) *                      (s - b) * (s - c));  }    // Driver Code int main()  {      float a = 3.0;      float b = 4.0;      float c = 5.0;        cout << "Area is " << findArea(a, b, c);      return 0;  }    // This code is contributed  // by rathbhupendra

## C

 #include  #include    float findArea(float a, float b, float c) {     // Length of sides must be positive and sum of any two sides     // must be smaller than third side.     if (a < 0 || b < 0 || c <0 || (a+b <= c) ||         a+c <=b || b+c <=a)     {         printf("Not a valid triangle");         exit(0);     }     float s = (a+b+c)/2;     return sqrt(s*(s-a)*(s-b)*(s-c)); }   int main() {     float a = 3.0;     float b = 4.0;     float c = 5.0;       printf("Area is %f", findArea(a, b, c));     return 0; }

## Java

 // Java program to print // Floyd's triangle       class Test {     static float findArea(float a, float b, float c)     {         // Length of sides must be positive and sum of any two sides         // must be smaller than third side.         if (a < 0 || b < 0 || c <0 || (a+b <= c) ||             a+c <=b || b+c <=a)         {             System.out.println("Not a valid triangle");             System.exit(0);         }         float s = (a+b+c)/2;         return (float)Math.sqrt(s*(s-a)*(s-b)*(s-c));     }               // Driver method     public static void main(String[] args)      {         float a = 3.0f;         float b = 4.0f;         float c = 5.0f;               System.out.println("Area is " + findArea(a, b, c));     } }

## Python3

 # Python Program to find the area  # of triangle    # Length of sides must be positive  # and sum of any two sides  def findArea(a,b,c):        # must be smaller than third side.      if (a < 0 or b < 0 or c < 0 or (a+b <= c) or (a+c <=b) or (b+c <=a) ):          print('Not a valid triangle')          return               # calculate the semi-perimeter      s = (a + b + c) / 2           # calculate the area      area = (s * (s - a) * (s - b) * (s - c)) ** 0.5     print('Area of a triangle is %f' %area)      # Initialize first side of triangle  a = 3.0 # Initialize second side of triangle  b = 4.0 # Initialize Third side of triangle  c = 5.0 findArea(a,b,c)    # This code is contributed by Shariq Raza

## C#

 // C# program to print // Floyd's triangle using System;   class Test {           // Function to find area     static float findArea(float a, float b,                         float c)     {                   // Length of sides must be positive         // and sum of any two sides         // must be smaller than third side.         if (a < 0 || b < 0 || c <0 ||          (a + b <= c) || a + c <=b ||              b + c <=a)         {             Console.Write("Not a valid triangle");             System.Environment.Exit(0);         }         float s = (a + b + c) / 2;         return (float)Math.Sqrt(s * (s - a) *                              (s - b) * (s - c));     }               // Driver code     public static void Main()      {         float a = 3.0f;         float b = 4.0f;         float c = 5.0f;               Console.Write("Area is " + findArea(a, b, c));     } }   // This code is contributed Nitin Mittal.

## PHP

 

## Javascript

 

Output

Area is 6

Time Complexity: O(log2n)
Auxiliary Space: O(1), since no extra space has been taken.

### Given the coordinates of the vertices of a triangle, the task is to find the area of this triangle.

Approach: If given coordinates of three corners, we can apply the Shoelace formula for the area below.

## C++

 // C++ program to evaluate area of a polygon using // shoelace formula #include  using namespace std;    // (X[i], Y[i]) are coordinates of i'th point. double polygonArea(double X[], double Y[], int n) {     // Initialize area     double area = 0.0;        // Calculate value of shoelace formula     int j = n - 1;     for (int i = 0; i < n; i++)     {         area += (X[j] + X[i]) * (Y[j] - Y[i]);         j = i;  // j is previous vertex to i     }        // Return absolute value     return abs(area / 2.0); }    // Driver program to test above function int main() {     double X[] = {0, 2, 4};     double Y[] = {1, 3, 7};        int n = sizeof(X)/sizeof(X[0]);        cout << polygonArea(X, Y, n); }

## Java

 // Java program to evaluate area of  // a polygon usingshoelace formula import java.io.*; import java.math.*;   class GFG {       // (X[i], Y[i]) are coordinates of i'th point.     static double polygonArea(double X[], double Y[], int n)     {         // Initialize area         double area = 0.0;               // Calculate value of shoelace formula         int j = n - 1;         for (int i = 0; i < n; i++)         {             area += (X[j] + X[i]) * (Y[j] - Y[i]);                           // j is previous vertex to i             j = i;          }               // Return absolute value         return Math.abs(area / 2.0);     }           // Driver program      public static void main (String[] args)      {         double X[] = {0, 2, 4};         double Y[] = {1, 3, 7};           int n = X.length;         System.out.println(polygonArea(X, Y, n));     } }     // This code is contributed // by Nikita Tiwari.

## Python3

 # Python 3 program to evaluate # area of a polygon using # shoelace formula   # (X[i], Y[i]) are coordinates of i'th point. def polygonArea(X,Y, n) :       # Initialize area     area = 0.0         # Calculate value of shoelace formula     j = n - 1     for i in range( 0, n) :         area = area + (X[j] + X[i]) * (Y[j] - Y[i])         j = i  # j is previous vertex to i                 # Return absolute value     return abs(area // 2.0)       # Driver program to test above function X = [0, 2, 4] Y = [1, 3, 7]   n = len(X) print(polygonArea(X, Y, n))     # This code is contributed # by Nikita Tiwari.

## C#

 // C# program to evaluate area of  // a polygon usingshoelace formula using System;   class GFG {       // (X[i], Y[i]) are coordinates      // of i'th point.     static double polygonArea(double []X,                        double []Y, int n)     {         // Initialize area         double area = 0.0;               // Calculate value of shoelace         // formula         int j = n - 1;         for (int i = 0; i < n; i++)         {             area += (X[j] + X[i]) *                          (Y[j] - Y[i]);                           // j is previous vertex to i             j = i;          }               // Return absolute value         return Math.Abs(area / 2.0);     }           // Driver program      public static void Main ()      {         double []X = {0, 2, 4};         double []Y = {1, 3, 7};           int n = X.Length;         Console.WriteLine(                  polygonArea(X, Y, n));     } }   // This code is contributed by anuj_67.

## PHP

 

## Javascript

 

Output

2

Time Complexity: O(n)
Auxiliary Space: O(1)

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