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.