Pentagon

A pentagon is a polygon with five sides and five angles. In a regular pentagon, all sides and angles are equal.

Properties of a Pentagon

1. Number of Sides: A pentagon has 5 sides.
2. Number of Angles: A pentagon has 5 angles.
3. Sum of Interior Angles: The sum of the interior angles of a pentagon is 540 degrees.
4. Sum of Exterior Angles: The sum of the exterior angles of a pentagon is always 360 degrees.
5. Types of Pentagons: There are regular and irregular pentagons. In a regular pentagon, all sides and angles are equal, while in an irregular pentagon, the sides and angles can have different measures.

Formulas for a Regular Pentagon

For a regular pentagon:

• Perimeter: P = 5 * s (where s is the length of each side)
• Interior Angle: A = 108°
• Apotem: a = s / (2 * tan(π/5))
• Area: A = (5/2) * a * s (where a is the apotem)

Practice Questions

1. Calculate the perimeter of a regular pentagon with each side measuring 8 cm.
2. Find the measure of each interior angle of a regular pentagon.
3. Determine the area of a regular pentagon with a side length of 10 cm.

By understanding the properties and formulas of a pentagon, you can solve problems and calculations related to this geometric shape.