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Find the altitude and area of an isosceles triangle
  • Last Updated : 06 Nov, 2020

Given the side (a) of the isosceles triangle. The task is to find the area (A) and the altitude (h). An isosceles triangle is a triangle with 2 sides of equal length and 2 equal internal angles adjacent to each equal sides.
 

In this figure, 
a- Measure of the equal sides of an isosceles triangle. 
b- Base of the isosceles triangle. 
h- Altitude of the isosceles triangle.

Examples: 

Input: a = 2, b = 3
Output: altitude = 1.32, area = 1.98

Input: a = 5, b = 6
Output: altitude = 4, area = 12

Formulas: Following are the formulas of the altitude and the area of an isosceles triangle.  



    $$ Altitude (h)= \sqrt{a^{2}- \frac{b^{2}}{2}} $$

[Tex]$$ Area (A)= \frac{1}{2} \times b \times h $$  [/Tex]

Below is the implementation using the above formulas: 

C++




// CPP program to find the Altitude
// Area of an isosceles triangle
#include <bits/stdc++.h>
using namespace std;
 
// function to find the atitude
float altitude(float a, float b)
{
    // return altitude
    return sqrt(pow(a, 2) - (pow(b, 2) / 4));
}
 
// function to find the area
float area(float b, float h)
{
 
    // return area
    return (1 * b * h) / 2;
}
 
// Driver code
int main()
{
 
    float a = 2, b = 3;
    float h = altitude(a, b);
    cout << setprecision(3);
    cout << "Altitude= " << h << ", ";
 
    cout << "Area= " << area(b, h);
    return 0;
}


Java




// Java program to find the Altitude
// Area of an isosceles triangle
 
import java.io.*;
 
class GFG {
 
    // function to find the atitude
    static float altitude(float a, float b)
    {
        // return altitude
        return (float)(Math.sqrt(Math.pow(a, 2)
                                 - (Math.pow(b, 2) / 4)));
    }
 
    // function to find the area
    static float area(float b, float h)
    {
 
        // return area
        return (1 * b * h) / 2;
    }
 
    // Driver Code
 
    public static void main(String[] args)
    {
        float a = 2, b = 3;
        float h = altitude(a, b);
        System.out.print("Altitude= " + h + ", ");
 
        System.out.print("Area= " + area(b, h));
    }
}
// This code is contributed by  inder_verma.


Python 3




# Python 3 program to find
# the Altitude Area of an
# isosceles triangle
import math
 
# function to find the atitude
 
 
def altitude(a, b):
 
    # return altitude
    return math.sqrt(pow(a, 2) -
                     (pow(b, 2) / 4))
 
# function to find the area
 
 
def area(b, h):
 
    # return area
    return (1 * b * h) / 2
 
 
# Driver Code
if __name__ == "__main__":
 
    a = 2
    b = 3
    h = altitude(a, b)
    print("Altitude = " +
          str(round(h, 3)), end=", ")
 
    print("Area = " +
          str(round(area(b, h), 3)))
 
# This code is contributed
# by ChitraNayal


C#




// C# program to find the Altitude
// Area of an isosceles triangle
using System;
 
class GFG {
 
    // function to find the atitude
    static float altitude(float a, float b)
    {
        // return altitude
        return (float)(Math.Sqrt(Math.Pow(a, 2)
                                 - (Math.Pow(b, 2) / 4)));
    }
 
    // function to find the area
    static float area(float b, float h)
    {
 
        // return area
        return (1 * b * h) / 2;
    }
 
    // Driver Code
    public static void Main()
    {
        float a = 2, b = 3;
        float h = altitude(a, b);
        Console.WriteLine("Altitude = " + h + ", ");
 
        Console.WriteLine("Area = " + area(b, h));
    }
}
 
// This code is contributed
// by inder_verma


PHP




<?php
// PHP program to find the Altitude
// Area of an isosceles triangle
 
// function to find the atitude
function altitude($a, $b)
{
    // return altitude
    return sqrt(pow($a, 2) -
               (pow($b, 2) / 4));
}
 
// function to find the area
function area($b, $h)
{
 
    // return area
    return (1 * $b * $h) / 2;
}
 
// Driver Code
$a = 2; $b = 3;
$h = altitude($a, $b);
 
echo "Altitude = " , $h , ", ";
 
echo "Area = " , area($b, $h);
 
// This code is contributed
// by anuj_67
?>


Output

Altitude= 1.32, Area= 1.98

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

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