Program to find area of a triangle

0 0 7 minutes read

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

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

#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#

// 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); 
} 

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

<?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)

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