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.

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

Area of a regular pentagon:

A = (5/4) * s^{2} * (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

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

Solution:

A = (5/4) * 8^{2} * (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

- Find the area of a regular pentagon with a side length of 10 units.
- Find the perimeter of a pentagon with a side length of 12 cm.
- 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.

.Study GuideShapes Worksheet/Answer key

Shapes Worksheet/Answer key

Shapes Worksheet/Answer key

Shapes Worksheet/Answer key

Shapes Worksheet/Answer key

Shapes Worksheet/Answer key

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Shapes Vocabulary/Answer key

Shapes Vocabulary/Answer key

Shapes

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.

Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life.