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: \(360° \div 5 = 72°\)

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