Pentagon

A pentagon is a five-sided polygon. In a regular pentagon, all sides and angles are equal. The sum of the interior angles of a pentagon is 540 degrees.

Properties of a Pentagon:

• Number of sides: 5
• Sum of interior angles: 540 degrees
• Diagonals: 5
• Regular pentagon: all sides and angles are equal

Formulas:

Area of a regular pentagon:
A = (5/4) * s² * (1/tan(π/5))
where s is the length of a side

Perimeter of a pentagon:
P = 5s
where s is the length of a side

Examples:

Example 1: Find the area of a regular pentagon with a side length of 8 units.

Solution:
A = (5/4) * 8² * (1/tan(π/5))
A ≈ 110.11 square units

Example 2: Find the perimeter of a pentagon with a side length of 6 cm.

Solution:
P = 5 * 6
P = 30 cm

Practice Problems:

1. Find the area of a regular pentagon with a side length of 10 units.
2. Find the perimeter of a pentagon with a side length of 12 cm.
3. If the interior angle of a pentagon measures 120 degrees, is it a regular pentagon?

Now that you have a better understanding of pentagons, practice solving problems and applying the formulas to become more familiar with this topic.