Area of Pentagram Given Long Chord Slice and Chord Length Calculator

Area of Pentagram Formula:

\[ A = \frac{\sqrt{5(5-2\sqrt{5})}}{2} \times (l_c - l_{\text{Long Chord Slice}})^2 \]

Area of Pentagram:

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1. What is the Area of Pentagram?

The Area of Pentagram is the total quantity of plane enclosed by the boundary of the entire Pentagram shape. It represents the two-dimensional space occupied by this geometric figure.

2. How Does the Calculator Work?

The calculator uses the Pentagram area formula:

\[ A = \frac{\sqrt{5(5-2\sqrt{5})}}{2} \times (l_c - l_{\text{Long Chord Slice}})^2 \]

Where:

\( A \) — Area of Pentagram (m²)
\( l_c \) — Chord Length of Pentagram (m)
\( l_{\text{Long Chord Slice}} \) — Long Chord Slice of Pentagram (m)

Explanation: The formula calculates the area based on the difference between the chord length and long chord slice, multiplied by a constant factor derived from the golden ratio properties of the pentagram.

3. Importance of Area Calculation

Details: Calculating the area of a pentagram is important in geometry, architectural design, and various mathematical applications where precise area measurements of complex shapes are required.

4. Using the Calculator

Tips: Enter chord length and long chord slice values in meters. Both values must be positive numbers, and the chord length must be greater than the long chord slice value.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagram?
A: A pentagram is a five-pointed star polygon formed by extending the sides of a regular pentagon until they intersect.

Q2: What are the Chord Length and Long Chord Slice?
A: The Chord Length is the diagonal length of the regular pentagon, while the Long Chord Slice is the edge length of the star shape or the equal side of the isosceles triangle forming the spike.

Q3: What units should I use for input values?
A: The calculator accepts values in meters, but you can use any consistent unit of length as the area will be in square units of that measurement.

Q4: Why is the chord length always greater than the long chord slice?
A: By definition, the chord length represents the full diagonal of the pentagon, while the long chord slice is only a portion of it, making the chord length necessarily larger.

Q5: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values with up to 4 decimal places for precise calculations.