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Write a Python function `area_tetrahedron(side)` that calculates the surface area of a regular tetrahedron given the length of its side. The formula for the surface area of a regular tetrahedron is:
\[ A = \sqrt{3} \times \text{side}^2 \]
#### Example Usage:
```python [main.nopy]
print(area_tetrahedron(3)) # Expected output: 15.588457268119894
print(area_tetrahedron(20)) # Expected output: 692.8203230275509
print(area_tetrahedron(10)) # Expected output: 173.20508075688772
```
#### Constraints:
- The input `side` will always be a positive number.
- Return the result as a floating-point number.import math
def area_tetrahedron(side):
"""
Calculate the surface area of a regular tetrahedron given the side length.
Args:
side (float): The length of a side of the tetrahedron.
Returns:
float: The surface area of the tetrahedron.
"""
# Placeholder for the implementation
pass