#### Area

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```"""
Find the area of various geometric shapes
Wikipedia reference: https://en.wikipedia.org/wiki/Area
"""
from math import pi, sqrt, tan

def surface_area_cube(side_length: float) -> float:
"""
Calculate the Surface Area of a Cube.

>>> surface_area_cube(1)
6
>>> surface_area_cube(1.6)
15.360000000000003
>>> surface_area_cube(0)
0
>>> surface_area_cube(3)
54
>>> surface_area_cube(-1)
Traceback (most recent call last):
...
ValueError: surface_area_cube() only accepts non-negative values
"""
if side_length < 0:
raise ValueError("surface_area_cube() only accepts non-negative values")
return 6 * side_length**2

def surface_area_cuboid(length: float, breadth: float, height: float) -> float:
"""
Calculate the Surface Area of a Cuboid.

>>> surface_area_cuboid(1, 2, 3)
22
>>> surface_area_cuboid(0, 0, 0)
0
>>> surface_area_cuboid(1.6, 2.6, 3.6)
38.56
>>> surface_area_cuboid(-1, 2, 3)
Traceback (most recent call last):
...
ValueError: surface_area_cuboid() only accepts non-negative values
>>> surface_area_cuboid(1, -2, 3)
Traceback (most recent call last):
...
ValueError: surface_area_cuboid() only accepts non-negative values
>>> surface_area_cuboid(1, 2, -3)
Traceback (most recent call last):
...
ValueError: surface_area_cuboid() only accepts non-negative values
"""
if length < 0 or breadth < 0 or height < 0:
raise ValueError("surface_area_cuboid() only accepts non-negative values")
return 2 * ((length * breadth) + (breadth * height) + (length * height))

"""
Calculate the Surface Area of a Sphere.
Wikipedia reference: https://en.wikipedia.org/wiki/Sphere
Formula: 4 * pi * r^2

>>> surface_area_sphere(5)
314.1592653589793
>>> surface_area_sphere(1)
12.566370614359172
>>> surface_area_sphere(1.6)
32.169908772759484
>>> surface_area_sphere(0)
0.0
>>> surface_area_sphere(-1)
Traceback (most recent call last):
...
ValueError: surface_area_sphere() only accepts non-negative values
"""
raise ValueError("surface_area_sphere() only accepts non-negative values")
return 4 * pi * radius**2

"""
Calculate the Surface Area of a Hemisphere.
Formula: 3 * pi * r^2

>>> surface_area_hemisphere(5)
235.61944901923448
>>> surface_area_hemisphere(1)
9.42477796076938
>>> surface_area_hemisphere(0)
0.0
>>> surface_area_hemisphere(1.1)
11.40398133253095
>>> surface_area_hemisphere(-1)
Traceback (most recent call last):
...
ValueError: surface_area_hemisphere() only accepts non-negative values
"""
raise ValueError("surface_area_hemisphere() only accepts non-negative values")
return 3 * pi * radius**2

def surface_area_cone(radius: float, height: float) -> float:
"""
Calculate the Surface Area of a Cone.
Wikipedia reference: https://en.wikipedia.org/wiki/Cone
Formula: pi * r * (r + (h ** 2 + r ** 2) ** 0.5)

>>> surface_area_cone(10, 24)
1130.9733552923256
>>> surface_area_cone(6, 8)
301.59289474462014
>>> surface_area_cone(1.6, 2.6)
23.387862992395807
>>> surface_area_cone(0, 0)
0.0
>>> surface_area_cone(-1, -2)
Traceback (most recent call last):
...
ValueError: surface_area_cone() only accepts non-negative values
>>> surface_area_cone(1, -2)
Traceback (most recent call last):
...
ValueError: surface_area_cone() only accepts non-negative values
>>> surface_area_cone(-1, 2)
Traceback (most recent call last):
...
ValueError: surface_area_cone() only accepts non-negative values
"""
if radius < 0 or height < 0:
raise ValueError("surface_area_cone() only accepts non-negative values")

def surface_area_conical_frustum(
) -> float:
"""
Calculate the Surface Area of a Conical Frustum.

>>> surface_area_conical_frustum(1, 2, 3)
45.511728065337266
>>> surface_area_conical_frustum(4, 5, 6)
300.7913575056268
>>> surface_area_conical_frustum(0, 0, 0)
0.0
>>> surface_area_conical_frustum(1.6, 2.6, 3.6)
78.57907060751548
>>> surface_area_conical_frustum(-1, 2, 3)
Traceback (most recent call last):
...
ValueError: surface_area_conical_frustum() only accepts non-negative values
>>> surface_area_conical_frustum(1, -2, 3)
Traceback (most recent call last):
...
ValueError: surface_area_conical_frustum() only accepts non-negative values
>>> surface_area_conical_frustum(1, 2, -3)
Traceback (most recent call last):
...
ValueError: surface_area_conical_frustum() only accepts non-negative values
"""
if radius_1 < 0 or radius_2 < 0 or height < 0:
raise ValueError(
"surface_area_conical_frustum() only accepts non-negative values"
)

def surface_area_cylinder(radius: float, height: float) -> float:
"""
Calculate the Surface Area of a Cylinder.
Wikipedia reference: https://en.wikipedia.org/wiki/Cylinder
Formula: 2 * pi * r * (h + r)

>>> surface_area_cylinder(7, 10)
747.6990515543707
>>> surface_area_cylinder(1.6, 2.6)
42.22300526424682
>>> surface_area_cylinder(0, 0)
0.0
>>> surface_area_cylinder(6, 8)
527.7875658030853
>>> surface_area_cylinder(-1, -2)
Traceback (most recent call last):
...
ValueError: surface_area_cylinder() only accepts non-negative values
>>> surface_area_cylinder(1, -2)
Traceback (most recent call last):
...
ValueError: surface_area_cylinder() only accepts non-negative values
>>> surface_area_cylinder(-1, 2)
Traceback (most recent call last):
...
ValueError: surface_area_cylinder() only accepts non-negative values
"""
if radius < 0 or height < 0:
raise ValueError("surface_area_cylinder() only accepts non-negative values")

"""Calculate the Area of a Torus.
Wikipedia reference: https://en.wikipedia.org/wiki/Torus
>>> surface_area_torus(1, 1)
39.47841760435743
>>> surface_area_torus(4, 3)
473.7410112522892
>>> surface_area_torus(3, 4)
Traceback (most recent call last):
...
ValueError: surface_area_torus() does not support spindle or self intersecting tori
>>> surface_area_torus(1.6, 1.6)
101.06474906715503
>>> surface_area_torus(0, 0)
0.0
>>> surface_area_torus(-1, 1)
Traceback (most recent call last):
...
ValueError: surface_area_torus() only accepts non-negative values
>>> surface_area_torus(1, -1)
Traceback (most recent call last):
...
ValueError: surface_area_torus() only accepts non-negative values
"""
raise ValueError("surface_area_torus() only accepts non-negative values")
raise ValueError(
"surface_area_torus() does not support spindle or self intersecting tori"
)

def area_rectangle(length: float, width: float) -> float:
"""
Calculate the area of a rectangle.

>>> area_rectangle(10, 20)
200
>>> area_rectangle(1.6, 2.6)
4.16
>>> area_rectangle(0, 0)
0
>>> area_rectangle(-1, -2)
Traceback (most recent call last):
...
ValueError: area_rectangle() only accepts non-negative values
>>> area_rectangle(1, -2)
Traceback (most recent call last):
...
ValueError: area_rectangle() only accepts non-negative values
>>> area_rectangle(-1, 2)
Traceback (most recent call last):
...
ValueError: area_rectangle() only accepts non-negative values
"""
if length < 0 or width < 0:
raise ValueError("area_rectangle() only accepts non-negative values")
return length * width

def area_square(side_length: float) -> float:
"""
Calculate the area of a square.

>>> area_square(10)
100
>>> area_square(0)
0
>>> area_square(1.6)
2.5600000000000005
>>> area_square(-1)
Traceback (most recent call last):
...
ValueError: area_square() only accepts non-negative values
"""
if side_length < 0:
raise ValueError("area_square() only accepts non-negative values")
return side_length**2

def area_triangle(base: float, height: float) -> float:
"""
Calculate the area of a triangle given the base and height.

>>> area_triangle(10, 10)
50.0
>>> area_triangle(1.6, 2.6)
2.08
>>> area_triangle(0, 0)
0.0
>>> area_triangle(-1, -2)
Traceback (most recent call last):
...
ValueError: area_triangle() only accepts non-negative values
>>> area_triangle(1, -2)
Traceback (most recent call last):
...
ValueError: area_triangle() only accepts non-negative values
>>> area_triangle(-1, 2)
Traceback (most recent call last):
...
ValueError: area_triangle() only accepts non-negative values
"""
if base < 0 or height < 0:
raise ValueError("area_triangle() only accepts non-negative values")
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(0, 0, 0)
0.0
>>> area_triangle_three_sides(1.6, 2.6, 3.6)
1.8703742940919619
>>> 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
>>> area_triangle_three_sides(2, 4, 7)
Traceback (most recent call last):
...
ValueError: Given three sides do not form a triangle
>>> area_triangle_three_sides(2, 7, 4)
Traceback (most recent call last):
...
ValueError: Given three sides do not form a triangle
>>> area_triangle_three_sides(7, 2, 4)
Traceback (most recent call last):
...
ValueError: Given three sides do not form a triangle
"""
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.

>>> area_parallelogram(10, 20)
200
>>> area_parallelogram(1.6, 2.6)
4.16
>>> area_parallelogram(0, 0)
0
>>> area_parallelogram(-1, -2)
Traceback (most recent call last):
...
ValueError: area_parallelogram() only accepts non-negative values
>>> area_parallelogram(1, -2)
Traceback (most recent call last):
...
ValueError: area_parallelogram() only accepts non-negative values
>>> area_parallelogram(-1, 2)
Traceback (most recent call last):
...
ValueError: area_parallelogram() only accepts non-negative values
"""
if base < 0 or height < 0:
raise ValueError("area_parallelogram() only accepts non-negative values")
return base * height

def area_trapezium(base1: float, base2: float, height: float) -> float:
"""
Calculate the area of a trapezium.

>>> area_trapezium(10, 20, 30)
450.0
>>> area_trapezium(1.6, 2.6, 3.6)
7.5600000000000005
>>> area_trapezium(0, 0, 0)
0.0
>>> area_trapezium(-1, -2, -3)
Traceback (most recent call last):
...
ValueError: area_trapezium() only accepts non-negative values
>>> area_trapezium(-1, 2, 3)
Traceback (most recent call last):
...
ValueError: area_trapezium() only accepts non-negative values
>>> area_trapezium(1, -2, 3)
Traceback (most recent call last):
...
ValueError: area_trapezium() only accepts non-negative values
>>> area_trapezium(1, 2, -3)
Traceback (most recent call last):
...
ValueError: area_trapezium() only accepts non-negative values
>>> area_trapezium(-1, -2, 3)
Traceback (most recent call last):
...
ValueError: area_trapezium() only accepts non-negative values
>>> area_trapezium(1, -2, -3)
Traceback (most recent call last):
...
ValueError: area_trapezium() only accepts non-negative values
>>> area_trapezium(-1, 2, -3)
Traceback (most recent call last):
...
ValueError: area_trapezium() only accepts non-negative values
"""
if base1 < 0 or base2 < 0 or height < 0:
raise ValueError("area_trapezium() only accepts non-negative values")
return 1 / 2 * (base1 + base2) * height

"""
Calculate the area of a circle.

>>> area_circle(20)
1256.6370614359173
>>> area_circle(1.6)
8.042477193189871
>>> area_circle(0)
0.0
>>> area_circle(-1)
Traceback (most recent call last):
...
ValueError: area_circle() only accepts non-negative values
"""
raise ValueError("area_circle() only accepts non-negative values")

"""
Calculate the area of a ellipse.

>>> area_ellipse(10, 10)
314.1592653589793
>>> area_ellipse(10, 20)
628.3185307179587
>>> area_ellipse(0, 0)
0.0
>>> area_ellipse(1.6, 2.6)
13.06902543893354
>>> area_ellipse(-10, 20)
Traceback (most recent call last):
...
ValueError: area_ellipse() only accepts non-negative values
>>> area_ellipse(10, -20)
Traceback (most recent call last):
...
ValueError: area_ellipse() only accepts non-negative values
>>> area_ellipse(-10, -20)
Traceback (most recent call last):
...
ValueError: area_ellipse() only accepts non-negative values
"""
raise ValueError("area_ellipse() only accepts non-negative values")

def area_rhombus(diagonal_1: float, diagonal_2: float) -> float:
"""
Calculate the area of a rhombus.

>>> area_rhombus(10, 20)
100.0
>>> area_rhombus(1.6, 2.6)
2.08
>>> area_rhombus(0, 0)
0.0
>>> area_rhombus(-1, -2)
Traceback (most recent call last):
...
ValueError: area_rhombus() only accepts non-negative values
>>> area_rhombus(1, -2)
Traceback (most recent call last):
...
ValueError: area_rhombus() only accepts non-negative values
>>> area_rhombus(-1, 2)
Traceback (most recent call last):
...
ValueError: area_rhombus() only accepts non-negative values
"""
if diagonal_1 < 0 or diagonal_2 < 0:
raise ValueError("area_rhombus() only accepts non-negative values")
return 1 / 2 * diagonal_1 * diagonal_2

def area_reg_polygon(sides: int, length: float) -> float:
"""
Calculate the area of a regular polygon.
Wikipedia reference: https://en.wikipedia.org/wiki/Polygon#Regular_polygons
Formula: (n*s^2*cot(pi/n))/4

>>> area_reg_polygon(3, 10)
43.301270189221945
>>> area_reg_polygon(4, 10)
100.00000000000001
>>> area_reg_polygon(0, 0)
Traceback (most recent call last):
...
ValueError: area_reg_polygon() only accepts integers greater than or equal to \
three as number of sides
>>> area_reg_polygon(-1, -2)
Traceback (most recent call last):
...
ValueError: area_reg_polygon() only accepts integers greater than or equal to \
three as number of sides
>>> area_reg_polygon(5, -2)
Traceback (most recent call last):
...
ValueError: area_reg_polygon() only accepts non-negative values as \
length of a side
>>> area_reg_polygon(-1, 2)
Traceback (most recent call last):
...
ValueError: area_reg_polygon() only accepts integers greater than or equal to \
three as number of sides
"""
if not isinstance(sides, int) or sides < 3:
raise ValueError(
"area_reg_polygon() only accepts integers greater than or \
equal to three as number of sides"
)
elif length < 0:
raise ValueError(
"area_reg_polygon() only accepts non-negative values as \
length of a side"
)
return (sides * length**2) / (4 * tan(pi / sides))
return (sides * length**2) / (4 * tan(pi / sides))

if __name__ == "__main__":
import doctest

doctest.testmod(verbose=True)  # verbose so we can see methods missing tests

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"Rhombus: {area_rhombus(10, 20) = }")
print(f"Trapezium: {area_trapezium(10, 20, 30) = }")
print(f"Circle: {area_circle(20) = }")
print(f"Ellipse: {area_ellipse(10, 20) = }")
print("\nSurface Areas of various geometric shapes: \n")
print(f"Cube: {surface_area_cube(20) = }")
print(f"Cuboid: {surface_area_cuboid(10, 20, 30) = }")
print(f"Sphere: {surface_area_sphere(20) = }")
print(f"Hemisphere: {surface_area_hemisphere(20) = }")
print(f"Cone: {surface_area_cone(10, 20) = }")
print(f"Conical Frustum: {surface_area_conical_frustum(10, 20, 30) = }")
print(f"Cylinder: {surface_area_cylinder(10, 20) = }")
print(f"Torus: {surface_area_torus(20, 10) = }")
print(f"Equilateral Triangle: {area_reg_polygon(3, 10) = }")
print(f"Square: {area_reg_polygon(4, 10) = }")
print(f"Reqular Pentagon: {area_reg_polygon(5, 10) = }")
```