SOLUTION: 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.

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): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~~~~~

As I read this post by @CPhill, it saddens me to see how clumsily the problem is formulated
and how poorly the solution is presented.

The part " hexagon has a perimeter of p " is totally irrelevant to the problem and should be omitted.

The normal formulation to this problem is as follow

A regular hexagon has the area of 3/2 square units. Find the side length of the hexagon.

Below is a normal mathematical solution in a form as it should be.

Let 'a' be the side length of the regular hexagon. This hexagon is the union of 6 equilateral triangles with the side length of 'a'. So, the area of each such a triangle is = of the square unit. The area of each such a triangle is . So, for 'a' we have this equation = , which implies = , a = = 3^(-1/4) = 0.7598 (rounded). ANSWER. The side of the regular hexagon is a = = 3^(-1/4) = 0.7598 (rounded). CHECK. = 1.49986 for the full area, which is a good approximation.

Solved.

Compare this solution with the mess of words in the post by @CPhill.

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