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

There are two main types of pentagons:

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

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.

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

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?

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.

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

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

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.