Area of Polygram Calculator

Area of Polygram Formula:

\[ A = \frac{N_{spikes} \times l_{base}^2}{4 \times \tan(\pi/N_{spikes})} + \frac{N_{spikes} \times h_{spike} \times l_{base}}{2} \]

Area of Polygram:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Area of Polygram?

The Area of Polygram is the total quantity of plane enclosed by the boundary of Polygram shape. A polygram is a geometric figure consisting of a regular polygon with isosceles triangular spikes attached to each side.

2. How Does the Calculator Work?

The calculator uses the Polygram area formula:

\[ A = \frac{N_{spikes} \times l_{base}^2}{4 \times \tan(\pi/N_{spikes})} + \frac{N_{spikes} \times h_{spike} \times l_{base}}{2} \]

Where:

\( N_{spikes} \) — Number of spikes in polygram
\( l_{base} \) — Base length of polygram (m)
\( h_{spike} \) — Spike height of polygram (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \tan \) — Tangent trigonometric function

Explanation: The formula calculates the combined area of the central polygon and all the triangular spikes that form the polygram shape.

3. Importance of Area Calculation

Details: Calculating the area of polygrams is important in geometry, architectural design, and various engineering applications where complex geometric shapes are used.

4. Using the Calculator

Tips: Enter the number of spikes (minimum 3), base length in meters, and spike height in meters. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the minimum number of spikes required?
A: The minimum number of spikes is 3, as a polygram must have at least three sides to form a closed shape.

Q2: Can the spike height be zero?
A: Yes, if spike height is zero, the polygram becomes a regular polygon without spikes.

Q3: What units should I use for measurements?
A: The calculator uses meters for length measurements, but you can use any consistent unit as long as all measurements are in the same unit.

Q4: Are there limitations to this formula?
A: This formula assumes regular polygrams with equal spike heights and base lengths. It may not be accurate for irregular polygrams.

Q5: How precise are the calculations?
A: The calculator provides results with up to 6 decimal places for accuracy in geometric calculations.