Regular Polygons Area

Overview

Engineering reference data for Regular Polygons Area in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Regular Polygons Area Data

Area Formulas with Different Variables

The area of a regular polygon can be calculated using different sets of known variables. The fundamental relationships are:

$A = \frac{n \cdot a \cdot r}{2} = n \cdot r^2 \tan\left(\frac{\pi}{n}\right) = \frac{n \cdot R^2 \sin\left(\frac{2\pi}{n}\right)}{2}$

Where:

• $A$ = area
• $n$ = number of sides
• $a$ = side length
• $r$ = apothem (inradius)
• $R$ = circumradius
• $\Theta = \pi/n$ (central angle for one segment)

The first form ($n \cdot a \cdot r / 2$) is often the most practical for construction when the apothem is known. The other forms are useful when working from the polygon's central geometry or when the side length is not directly available. Refer to the Variables section for the full definitions of these terms.

Interactive Charts

References

• Original Source