Polygon Area

Source: May 2025, Task 1 (DTU 02002/02003). Study solution — not an official answer key.

Problem

The area of a regular polygon with n sides of length s is:

A = (n * s2) / (4 * tan(π / n))

Write polygon_area(n, s) that returns this area as a float.

• n: int — number of sides
• s: float — side length
• Returns: float — polygon area

>>> polygon_area(5, 4.31)
31.9597602410807

Approach

Use math.tan and math.pi. Apply the formula directly.

Solution

import math

def polygon_area(n, s):
    return (n * s ** 2) / (4 * math.tan(math.pi / n))