Area of Pentagram Calculator

Area of Pentagram Formula:

\[ A = \frac{\sqrt{5(5 - 2\sqrt{5})} \times l_e^2}{2} \]

Area of Pentagram:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Area of Pentagram?

The Area of Pentagram refers to the total quantity of plane enclosed by the boundary of the entire Pentagram shape. A pentagram is constructed from the diagonals of a regular pentagon.

2. How Does the Calculator Work?

The calculator uses the Area of Pentagram formula:

\[ A = \frac{\sqrt{5(5 - 2\sqrt{5})} \times l_e^2}{2} \]

Where:

\( A \) — Area of Pentagram (m²)
\( l_e \) — Pentagonal Edge Length of Pentagram (m)

Explanation: This formula calculates the area of a pentagram based on the edge length of the regular pentagon from which it is constructed.

3. Importance of Area Calculation

Details: Calculating the area of geometric shapes like pentagrams is fundamental in geometry, architecture, design, and various mathematical applications.

4. Using the Calculator

Tips: Enter the pentagonal edge length in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a pentagram?
A: A pentagram is a five-pointed star polygon, formed by drawing the diagonals of a regular pentagon.

Q2: What units should I use for the input?
A: The calculator uses meters as the default unit, but you can use any consistent unit of length as the area will be in square units of that measurement.

Q3: Can this formula be used for irregular pentagrams?
A: No, this formula is specifically for regular pentagrams constructed from regular pentagons.

Q4: What is the relationship between pentagon and pentagram?
A: A pentagram is created by connecting every other vertex of a regular pentagon with straight lines.

Q5: Are there other ways to calculate pentagram area?
A: Yes, the area can also be calculated using the chord lengths or other geometric properties, but this formula using the pentagonal edge length is one of the most straightforward methods.