Add function to calculate area of triangle using Heron's formula (TheAlgorithms#4065)

* Update area.py

Modified area of triangle function. Added a new algorithm to calculate area when 3 sides are known

* Add files via upload

* Update area.py

* Update area.py

* Update area.py

* Update area.py

* Remove unnecessary whitespace

Co-authored-by: Dhruv Manilawala <[email protected]>

Author: 2 people

maths/area.py

@@ -1,7 +1,7 @@
 """
 Find the area of various geometric shapes
 """
-from math import pi
+from math import pi, sqrt
 
 
 def surface_area_cube(side_length: float) -> float:
@@ -26,7 +26,7 @@ def surface_area_sphere(radius: float) -> float:
     """
     Calculate the Surface Area of a Sphere.
     Wikipedia reference: https://en.wikipedia.org/wiki/Sphere
-    :return 4 * pi * r^2
+    Formula: 4 * pi * r^2
 
     >>> surface_area_sphere(5)
     314.1592653589793
@@ -44,7 +44,7 @@ def surface_area_sphere(radius: float) -> float:
 
 def area_rectangle(length: float, width: float) -> float:
     """
-    Calculate the area of a rectangle
+    Calculate the area of a rectangle.
 
     >>> area_rectangle(10, 20)
     200
@@ -68,7 +68,7 @@ def area_rectangle(length: float, width: float) -> float:
 
 def area_square(side_length: float) -> float:
     """
-    Calculate the area of a square
+    Calculate the area of a square.
 
     >>> area_square(10)
     100
@@ -84,7 +84,7 @@ def area_square(side_length: float) -> float:
 
 def area_triangle(base: float, height: float) -> float:
     """
-    Calculate the area of a triangle
+    Calculate the area of a triangle given the base and height.
 
     >>> area_triangle(10, 10)
     50.0
@@ -106,9 +106,42 @@ def area_triangle(base: float, height: float) -> float:
     return (base * height) / 2
 
 
+def area_triangle_three_sides(side1: float, side2: float, side3: float) -> float:
+    """
+    Calculate area of triangle when the length of 3 sides are known.
+
+    This function uses Heron's formula: https://en.wikipedia.org/wiki/Heron%27s_formula
+
+    >>> area_triangle_three_sides(5, 12, 13)
+    30.0
+    >>> area_triangle_three_sides(10, 11, 12)
+    51.521233486786784
+    >>> area_triangle_three_sides(-1, -2, -1)
+    Traceback (most recent call last):
+        ...
+    ValueError: area_triangle_three_sides() only accepts non-negative values
+    >>> area_triangle_three_sides(1, -2, 1)
+    Traceback (most recent call last):
+        ...
+    ValueError: area_triangle_three_sides() only accepts non-negative values
+    """
+    if side1 < 0 or side2 < 0 or side3 < 0:
+        raise ValueError("area_triangle_three_sides() only accepts non-negative values")
+    elif side1 + side2 < side3 or side1 + side3 < side2 or side2 + side3 < side1:
+        raise ValueError("Given three sides do not form a triangle")
+    semi_perimeter = (side1 + side2 + side3) / 2
+    area = sqrt(
+        semi_perimeter
+        * (semi_perimeter - side1)
+        * (semi_perimeter - side2)
+        * (semi_perimeter - side3)
+    )
+    return area
+
+
 def area_parallelogram(base: float, height: float) -> float:
     """
-    Calculate the area of a parallelogram
+    Calculate the area of a parallelogram.
 
     >>> area_parallelogram(10, 20)
     200
@@ -132,7 +165,7 @@ def area_parallelogram(base: float, height: float) -> float:
 
 def area_trapezium(base1: float, base2: float, height: float) -> float:
     """
-    Calculate the area of a trapezium
+    Calculate the area of a trapezium.
 
     >>> area_trapezium(10, 20, 30)
     450.0
@@ -172,7 +205,7 @@ def area_trapezium(base1: float, base2: float, height: float) -> float:
 
 def area_circle(radius: float) -> float:
     """
-    Calculate the area of a circle
+    Calculate the area of a circle.
 
     >>> area_circle(20)
     1256.6370614359173
@@ -188,7 +221,7 @@ def area_circle(radius: float) -> float:
 
 def area_ellipse(radius_x: float, radius_y: float) -> float:
     """
-    Calculate the area of a ellipse
+    Calculate the area of a ellipse.
 
     >>> area_ellipse(10, 10)
     314.1592653589793
@@ -214,7 +247,7 @@ def area_ellipse(radius_x: float, radius_y: float) -> float:
 
 def area_rhombus(diagonal_1: float, diagonal_2: float) -> float:
     """
-    Calculate the area of a rhombus
+    Calculate the area of a rhombus.
 
     >>> area_rhombus(10, 20)
     100.0
@@ -236,24 +269,20 @@ def area_rhombus(diagonal_1: float, diagonal_2: float) -> float:
     return 1 / 2 * diagonal_1 * diagonal_2
 
 
-def main():
-    print("Areas of various geometric shapes: \n")
-    print(f"Rectangle: {area_rectangle(10, 20)}")
-    print(f"Square: {area_square(10)}")
-    print(f"Triangle: {area_triangle(10, 10)}")
-    print(f"Parallelogram: {area_parallelogram(10, 20)}")
-    print(f"Trapezium: {area_trapezium(10, 20, 30)}")
-    print(f"Circle: {area_circle(20)}")
-    print("\nSurface Areas of various geometric shapes: \n")
-    print(f"Cube: {surface_area_cube(20)}")
-    print(f"Sphere: {surface_area_sphere(20)}")
-    print(f"Rhombus: {area_rhombus(10, 20)}")
-
-
 if __name__ == "__main__":
-
     import doctest
 
     doctest.testmod(verbose=True)  # verbose so we can see methods missing tests
 
-    main()
+    print("[DEMO] Areas of various geometric shapes: \n")
+    print(f"Rectangle: {area_rectangle(10, 20) = }")
+    print(f"Square: {area_square(10) = }")
+    print(f"Triangle: {area_triangle(10, 10) = }")
+    print(f"Triangle: {area_triangle_three_sides(5, 12, 13) = }")
+    print(f"Parallelogram: {area_parallelogram(10, 20) = }")
+    print(f"Trapezium: {area_trapezium(10, 20, 30) = }")
+    print(f"Circle: {area_circle(20) = }")
+    print("\nSurface Areas of various geometric shapes: \n")
+    print(f"Cube: {surface_area_cube(20) = }")
+    print(f"Sphere: {surface_area_sphere(20) = }")
+    print(f"Rhombus: {area_rhombus(10, 20) = }")