Find the altitude and area of an isosceles triangle

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.  

[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 altitude
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 altitude
    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 altitude


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 altitude
    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 altitude
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
?>

Javascript

<script>

// Javascript program to find the Altitude
// Area of an isosceles triangle

// function to find the altitude
function altitude(a,b)
{
    // return altitude
    return Math.sqrt(Math.pow(a, 2) - (Math.pow(b, 2) / 4));
}

// function to find the area
function area( b, h)
{

    // return area
    return (1 * b * h) / 2;
}

// Driver code
let a = 2, b = 3;
    let h = altitude(a, b);
    document.write("Altitude= " + h.toFixed(2) + ", ");

    document.write( "Area= " + area(b, h).toFixed(2));

// This code contributed by aashish1995

</script>

Output

Altitude= 1.32, Area= 1.98

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