Question 1210520
```python
import math

# A = (3 * sqrt(3) / 2) * s^2
# 3/2 = (3 * sqrt(3) / 2) * s^2
# 1 = sqrt(3) * s^2
# s^2 = 1 / sqrt(3)
# s = 1 / (3**(1/4))

s = 1 / (3**0.25)
print(f"s = {s}")
print(f"s^4 = {s**4}")
print(f"1/3 = {1/3}")



```

```text
s = 0.7598356856515925
s^4 = 0.3333333333333333
1/3 = 0.3333333333333333


```

To find the side length of a regular hexagon given its area, we use the standard area formula for a regular hexagon with side length .

### 1. The Area Formula

A regular hexagon can be divided into six equilateral triangles. The area of one equilateral triangle with side  is . Therefore, the total area  of the hexagon is:


### 2. Solving for the Side Length ()

We are given that the area . Substituting this into the formula:


To solve for , we divide both sides by :


Now, we take the square root of both sides to find :


Using exponent notation,  and . Thus:


### Summary

If the area  is exactly , the side length of the hexagon is:


*(Note: In many geometry problems, the area is given as . In that specific case, the side length would simplify to exactly ****. However, based on the value  provided, the side length is .)*