# Find the altitude and area of an isosceles triangle

• Last Updated : 21 Aug, 2022

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  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

 

## Javascript

 

Output

Altitude= 1.32, Area= 1.98

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

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