Result

Calculation Steps

Visual Representation

About Pentagons

What is a Pentagon?

A pentagon is a five-sided polygon with five vertices and five angles. In a regular pentagon, all sides are equal in length and all interior angles are equal.

Formulas

For a regular pentagon with side length $s$:

• Perimeter: $P=5s$
• Area: $A=\frac{1}{4}\sqrt{25+10\sqrt{5}}{s}^2$
• Interior angle: $\theta =\frac{(n-2)\times 180°}{n}=108°$
• Central angle: $360°÷5=72°$

Calculation Steps

1. Calculate the perimeter: $P=5s$
2. Calculate the area: $A=\frac{1}{4}\sqrt{25+10\sqrt{5}}{s}^2$
3. Calculate the apothem: $a=\frac{s}{2\tan (36°)}$

Example

Let's calculate the properties of a regular pentagon with side length 5 units:

1. Perimeter: $P=5\times 5=25$ units
2. Area: $A=\frac{1}{4}\sqrt{25+10\sqrt{5}}{5}^2\approx 43.01$ square units
3. Apothem: $a=\frac{5}{2\tan (36°)}\approx 3.44$ units