# Python Program to Find Isosceles Triangle Area

In the previous article, we have discussed Python Program to Find Volume and Surface Area of Sphere
Isosceles triangle :

An isosceles triangle is a triangle with two equal-length sides in geometry.It is sometimes stated as having exactly two equal-length sides and other times as having at least two equal-length sides, with the latter containing the equilateral triangle as a particular scenario.

Formula :

The formula to find the area of an isosceles triangle = (y * math.sqrt((4 * x * x) – (y * y)))/4;

where x , y are the two side lengths of an isosceles triangle.

Given two sides of an isosceles triangle and the task is to find the area of the given isosceles triangle.

Examples:

Example1:

Input:

Given length of first side = 5
Given length of second side = 9

Output:

The Given Isosceles Triangle area with sides [ 5 , 9 ]= 9.808

Example2:

Input:

Given length of first side =  12
Given length of second side = 17.2

Output:

The Given Isosceles Triangle area with sides [ 12 , 17.2 ]= 71.973

## Program to Find Isosceles Triangle Area

Below are the ways to find the area of the given isosceles triangle:

### Method #1: Using Mathematical Formula (Static Input)

Approach:

• Import math module using the import keyword.
• Give the length of the first side of an isosceles triangle as static input and store it in a variable.
• Give the length of the second side of an isosceles triangle as static input and store it in another variable.
• Calculate the length of the given isosceles triangle using math.sqrt() function and the above given mathematical formula.
• Store it in another variable.
• Print the area of the given isosceles triangle.
• The Exit of the Program.

Below is the implementation:

# Import math module using the import keyword.
import math
# Give the length of the first side of an isosceles triangle as static input
# and store it in a variable.
fst_side = 5
# Give the length of the second side of an isosceles triangle as static input
# and store it in another variable.
secnd_side = 9
# Calculate the length of the given isosceles triangle using math.sqrt() function
# and the above given mathematical formula.
# Store it in another variable.
area_isosce_tringl = (
secnd_side * math.sqrt((4 * fst_side * fst_side) - (secnd_side * secnd_side)))/4
# Print the area of the given isosceles triangle.
print("The Given Isosceles Triangle area with sides [",
fst_side, ",", secnd_side, "]= %.3f" % area_isosce_tringl)


Output:

The Given Isosceles Triangle area with sides [ 5 , 9 ]= 9.808

### Method #2: Using Mathematical Formula (User Input)

Approach:

• Import math module using the import keyword.
• Give the length of the first side of an isosceles triangle as user input using the float(input()) function and store it in a variable.
• Give the length of the second side of an isosceles triangle as user input using the float(input()) function and store it in another variable.
• Calculate the length of the given isosceles triangle using math.sqrt() function and the above given mathematical formula.
• Store it in another variable.
• Print the area of the given isosceles triangle.
• The Exit of the Program.

Below is the implementation:

# Import math module using the import keyword.
import math
# Give the length of the first side of an isosceles triangle as user input using the float(input())
#function and store it in a variable.
fst_side = float(input("Enter some random number = "))
# Give the length of the second side of an isosceles triangle as user input using the float(input())
#function and store it in another variable.
secnd_side =  float(input("Enter some random number = "))
# Calculate the length of the given isosceles triangle using math.sqrt() function
# and the above given mathematical formula.
# Store it in another variable.
area_isosce_tringl = (
secnd_side * math.sqrt((4 * fst_side * fst_side) - (secnd_side * secnd_side)))/4
# Print the area of the given isosceles triangle.
print("The Given Isosceles Triangle area with sides [",
fst_side, ",", secnd_side, "]= %.3f" % area_isosce_tringl)


Output:

Enter some random number = 15
Enter some random number = 22.5
The Given Isosceles Triangle area with sides [ 15.0 , 22.5 ]= 111.618

The area is isosceles is calculated by the above formula.

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