How to Find the Height of an Isosceles Triangle
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.
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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++
#include <bits/stdc++.h>
using namespace std;
float altitude( float a, float b)
{
return sqrt ( pow (a, 2) - ( pow (b, 2) / 4));
}
float area( float b, float h)
{
return (1 * b * h) / 2;
}
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
import java.io.*;
class GFG {
static float altitude( float a, float b)
{
return ( float )(Math.sqrt(Math.pow(a, 2 )
- (Math.pow(b, 2 ) / 4 )));
}
static float area( float b, float h)
{
return ( 1 * b * h) / 2 ;
}
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));
}
}
Python 3
import math
def altitude(a, b):
return math.sqrt( pow (a, 2 ) -
( pow (b, 2 ) / 4 ))
def area(b, h):
return ( 1 * b * h) / 2
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 )))
C#
using System;
class GFG {
static float altitude( float a, float b)
{
return ( float )(Math.Sqrt(Math.Pow(a, 2)
- (Math.Pow(b, 2) / 4)));
}
static float area( float b, float h)
{
return (1 * b * h) / 2;
}
public static void Main()
{
float a = 2, b = 3;
float h = altitude(a, b);
Console.WriteLine( "Altitude = " + h + ", " );
Console.WriteLine( "Area = " + area(b, h));
}
}
PHP
<?php
function altitude( $a , $b )
{
return sqrt(pow( $a , 2) -
(pow( $b , 2) / 4));
}
function area( $b , $h )
{
return (1 * $b * $h ) / 2;
}
$a = 2; $b = 3;
$h = altitude( $a , $b );
echo "Altitude = " , $h , ", " ;
echo "Area = " , area( $b , $h );
?>
Javascript
<script>
function altitude(a,b)
{
return Math.sqrt(Math.pow(a, 2) - (Math.pow(b, 2) / 4));
}
function area( b, h)
{
return (1 * b * h) / 2;
}
let a = 2, b = 3;
let h = altitude(a, b);
document.write( "Altitude= " + h.toFixed(2) + ", " );
document.write( "Area= " + area(b, h).toFixed(2));
</script>
Output
Altitude= 1.32, Area= 1.98
Time Complexity: O(log n)
Auxiliary Space: O(1)
How to Find the Height of an Isosceles Triangle
Source: https://www.geeksforgeeks.org/find-the-altitude-and-area-of-an-isosceles-triangle/