Question 1210520: A regular hexagon has a perimeter of p (in length units) and an area of A (in square units). If A=3/2 then find the side length of the hexagon.
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(2189)   (Show Source):
You can put this solution on YOUR website! ```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 .)*
Answer by ikleyn(53646)  (Show Source):
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