Write a formula for the area of an equilateral triangle as a function of a side length.

The area \( A \) of an equilateral triangle can be expressed as a function of its side length \( s \) using the following formula:

\[
A = \frac{\sqrt{3}}{4} s^2
\]

### Explanation:
- **Side length (\( s \))**: The length of any side of the equilateral triangle.
- **\(\sqrt{3}/4\)**: This is a constant derived from the geometric properties of an equilateral triangle.

This formula is derived by considering the triangle's height and using the basic formula for the area of a triangle, \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \).

Would you like more details on the derivation or have any questions?

### Related Questions:
1. How do you derive the formula for the area of an equilateral triangle?
2. What is the height of an equilateral triangle as a function of its side length?
3. How does the area of an equilateral triangle compare to a square with the same side length?
4. How would the formula change if the triangle was not equilateral but isosceles?
5. Can you generalize the area formula for any regular polygon?

### Tip:
When dealing with equilateral triangles, remember that all sides and angles are equal, which simplifies many calculations.

Discover how to calculate the area of an equilateral triangle using the formula A = (sqrt(3)/4) * s^2. This problem explores the geometric properties of equilateral triangles and provides step-by-step explanations. Suitable for Grades 7-9 students studying geometry.

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