1. What is the Pentagonal Pyramid Side Length Formula?

The formula calculates the side length of a regular pentagonal pyramid given its volume and height. It's derived from the volume formula of a pentagonal pyramid by solving for the side length.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( s \) — Side length of the pentagon base (m)
• \( V \) — Volume of the pyramid (m³)
• \( h \) — Height of the pyramid (m)
• \( \tan(54°) \) — Tangent of 54 degrees (internal angle of pentagon)

Explanation: The formula first calculates the area of the pentagonal base from the volume and height, then derives the side length from the pentagon's area.

3. Importance of Side Length Calculation

Details: Knowing the side length is crucial for construction, 3D modeling, and geometric calculations involving pentagonal pyramids.

4. Using the Calculator

Tips: Enter volume in cubic meters, height in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular pentagonal pyramid?
A: A pyramid with a regular pentagon base and five triangular faces meeting at the apex.

Q2: How accurate is this calculation?
A: The calculation is mathematically exact for perfect regular pentagonal pyramids.

Q3: Can I use different units?
A: Yes, but all inputs must be in consistent units (e.g., all in meters or all in feet).

Q4: What if my pyramid isn't regular?
A: This formula only works for regular pentagonal pyramids with equal side lengths and angles.

Q5: What's the relationship between side length and height?
A: For a given volume, side length decreases as height increases, following an inverse square root relationship.