Program to find area of a triangle

Last Updated : 23 Jul, 2025

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

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

$Area = \sqrt(s*(s-a)*(s-b)*(s-c))$

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

Try it on GfG Practice

Below is the implementation of the above approach:

C++

// C++ Program to find the area 
// of triangle 
#include <bits/stdc++.h>
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++ Program to find the area 
// of triangle #include <bits/stdc++.h>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 Codeint 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

#include <stdio.h> 
#include <stdlib.h> 

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# 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

<?php
function findArea($a, $b, $c)
{
    // Length of sides must be positive
    // and sum of any two sides must
    // be smaller than third side.
    if ($a < 0 or $b < 0 or
        $c < 0 or ($a + $b <= $c) or
        $a + $c <= $b or $b + $c <= $a)
    {
        echo "Not a valid triangle";
        exit(0);
    }
    $s = ($a + $b + $c) / 2;
    return sqrt($s * ($s - $a) * 
            ($s - $b) * ($s - $c));
}

// Driver Code
$a = 3.0;
$b = 4.0;
$c = 5.0;

echo "Area is ", findArea($a, $b, $c);

// This code is contributed anuJ_67.
?>

JavaScript

<script>

// javascript Program to find the area 
// of triangle 

function findArea( a,  b,  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) 
    { 
        document.write( "Not a valid triangle"); 
        return;
    } 
    let s = (a + b + c) / 2; 
    return Math.sqrt(s * (s - a) * 
                    (s - b) * (s - c)); 
} 

// Driver Code

    let a = 3.0; 
    let b = 4.0; 
    let c = 5.0; 

  document.write( "Area is " + findArea(a, b, c)); 

// This code is contributed by todaysgaurav 

</script>

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.

$Area = \frac{\sum_{i=1}^{n-1} (x_i y_{(i+1)}+x_ny_{1}) - \sum_{i=1}^{n-1}(x_{(i+1)}y_i-x_1y_n)}{2}$

$= \frac{(x_{1}y_{2} + x_{2}y_{3} + ... + x_{n-1}y_{n} + x_{n}y_{1}) -(x_{2}y_{1} + x_{3}y_{2} + ... + x_{n}y_{n-1} + x_{1}y_{n})}{2}$

C++

// C++ program to evaluate area of a polygon using
// shoelace formula
#include <bits/stdc++.h>
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);
}

 
// C++ program to evaluate area of a polygon using
// shoelace formula#include <bits/stdc++.h>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 functionint 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# 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

<?php
// PHP program to evaluate area of a 
// polygon using shoelace formula

// (X[i], Y[i]) are coordinates
// of i'th point.
function polygonArea( $X, $Y, $n)
{
    
    // Initialize area
    $area = 0.0;

    // Calculate value of 
    // shoelace formula
    $j = $n - 1;
    for ( $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 abs($area / 2.0);
}

    // Driver Code
    $X = array(0, 2, 4);
    $Y = array(1, 3, 7);
    $n = count($X);
    echo polygonArea($X, $Y, $n);

// This code is contributed by anuj_67.
?>

JavaScript

<script>

// Javascript program to evaluate area of a polygon using
// shoelace formula

// (X[i], Y[i]) are coordinates of i'th point.
function polygonArea(X, Y, n)
{

    // Initialize area
    let area = 0.0;

    // Calculate value of shoelace formula
    let j = n - 1;
    for (let 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 Math.abs(area / 2.0);
}

// Driver program to test above function
    let X = [0, 2, 4];
    let Y = [1, 3, 7];

    let n = X.length;

    document.write(polygonArea(X, Y, n));

// This code is contributed by Mayank Tyagi

</script>

Output

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

kartik

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Program to find area of a triangle

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

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

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