You can’t reliably find the surface area of literally any shape unless the shape is described somehow — for example:

• a known formula shape like a cube, sphere, cylinder, cone
• a 2D polygon with coordinates
• a 3D mesh made of triangles
• a mathematical function/surface

A good general Python design is to build an algorithm that chooses the right formula based on the shape type.

Here’s a clean starter version for common 3D shapes:

import math

def surface_area(shape, **kwargs):
    shape = shape.lower()

    if shape == "cube":
        side = kwargs["side"]
        return 6 * side ** 2

    elif shape == "rectangular_prism":
        length = kwargs["length"]
        width = kwargs["width"]
        height = kwargs["height"]
        return 2 * (length * width + length * height + width * height)

    elif shape == "sphere":
        radius = kwargs["radius"]
        return 4 * math.pi * radius ** 2

    elif shape == "cylinder":
        radius = kwargs["radius"]
        height = kwargs["height"]
        return 2 * math.pi * radius * (radius + height)

    elif shape == "cone":
        radius = kwargs["radius"]
        height = kwargs["height"]
        slant_height = math.sqrt(radius ** 2 + height ** 2)
        return math.pi * radius * (radius + slant_height)

    elif shape == "triangular_prism":
        base = kwargs["base"]
        triangle_height = kwargs["triangle_height"]
        prism_length = kwargs["length"]

        side_a = kwargs["side_a"]
        side_b = kwargs["side_b"]
        side_c = kwargs["side_c"]

        triangle_area = 0.5 * base * triangle_height
        perimeter = side_a + side_b + side_c

        return 2 * triangle_area + perimeter * prism_length

    else:
        raise ValueError("Shape not supported yet.")

Example usage:

print(surface_area("cube", side=5))

print(surface_area("sphere", radius=3))

print(surface_area("cylinder", radius=4, height=10))

print(surface_area(
    "rectangular_prism",
    length=8,
    width=4,
    height=2
))

Output would be:

150
113.09733552923255
351.85837720205683
112

If you want something closer to “any shape,” the most flexible method is to represent the shape as a 3D mesh made of triangles. Then the total surface area is just the sum of all triangle areas.

Here’s a generic triangle-mesh surface area algorithm:

import math

def distance(p1, p2):
    return math.sqrt(
        (p2[0] - p1[0]) ** 2 +
        (p2[1] - p1[1]) ** 2 +
        (p2[2] - p1[2]) ** 2
    )

def triangle_area(p1, p2, p3):
    a = distance(p1, p2)
    b = distance(p2, p3)
    c = distance(p3, p1)

    s = (a + b + c) / 2

    return math.sqrt(s * (s - a) * (s - b) * (s - c))

def mesh_surface_area(triangles):
    total_area = 0

    for triangle in triangles:
        p1, p2, p3 = triangle
        total_area += triangle_area(p1, p2, p3)

    return total_area

Example:

triangles = [
    ((0, 0, 0), (1, 0, 0), (0, 1, 0)),
    ((1, 0, 0), (1, 1, 0), (0, 1, 0))
]

print(mesh_surface_area(triangles))

This calculates the area of two triangles making a square, so the result is:

1.0

So the best answer is:

surface_area(shape, **dimensions)

for regular shapes, and:

mesh_surface_area(triangles)

for irregular 3D shapes.

👉 Are you trying to calculate surface area for basic geometry homework shapes, or for an irregular 3D model/object?