Pentagon Study Guide

Definition

A pentagon is a five-sided polygon. The sum of the interior angles of a pentagon is 540 degrees.

Types of Pentagons

There are two main types of pentagons:

1. Regular Pentagon: A regular pentagon has all its sides and angles equal in measure. Each interior angle of a regular pentagon measures 108 degrees.
2. Irregular Pentagon: An irregular pentagon has sides and/or angles of different measures.

Formulas and Properties

Here are some important formulas and properties related to pentagons:

• Perimeter: The perimeter of a pentagon is the sum of the lengths of its five sides.
• Area: The area of a regular pentagon can be calculated using the formula:
  \( \text{Area} = \frac{5}{2} \times \text{side length} \times \text{apothem length} \)
• Diagonals: A pentagon has five diagonals, which are the line segments connecting non-adjacent vertices.

Example Problems

1. Calculate the perimeter of a pentagon with side lengths of 8 cm, 6 cm, 8 cm, 6 cm, and 7 cm.
2. Find the area of a regular pentagon with a side length of 10 cm and an apothem length of 7.5 cm.
3. Determine the measure of each interior angle in a regular pentagon.

Practice Questions

1. Find the perimeter of a pentagon with side lengths of 12 cm, 9 cm, 12 cm, 9 cm, and 10 cm.

2. Calculate the area of a regular pentagon with a side length of 15 cm and an apothem length of 12 cm.

3. If the measure of one interior angle of a regular pentagon is 120 degrees, what is the measure of each exterior angle?

Conclusion

Studying the properties and formulas related to pentagons is important for solving problems involving these five-sided figures. Practice calculating perimeters, areas, and angle measures to strengthen your understanding of pentagons.

[Pentagon] Related Worksheets and Study Guides:

• The New MillenniumSocial Studies • Eighth Grade