Polygons Study Guide

What is a Polygon?

A polygon is a 2-dimensional shape that is formed by straight lines. It has straight sides and angles, and the sides do not cross each other.

Types of Polygons

There are different types of polygons based on the number of sides they have:

Triangle: 3 sides
Quadrilateral: 4 sides
Pentagon: 5 sides
Hexagon: 6 sides
Heptagon: 7 sides
Octagon: 8 sides
Nonagon: 9 sides
Decagon: 10 sides

Properties of Polygons

Some important properties of polygons include:

Number of Sides: Each polygon has a specific number of sides.
Interior Angles: The sum of the interior angles of a polygon with n sides is given by (n-2) * 180 degrees.
Exterior Angles: The sum of the exterior angles of any polygon, one angle at each vertex, is always 360 degrees.
Types of Polygons: Polygons can be classified as regular or irregular based on the congruency of their sides and angles.

Regular and Irregular Polygons

In a regular polygon, all sides are of equal length and all angles are of equal measure. In an irregular polygon, the sides and angles may have different lengths and measures.

Formula for Sum of Interior Angles

The formula to find the sum of the interior angles of a polygon with n sides is given by:

Sum of Interior Angles = (n-2) * 180 degrees

Formula for Exterior Angle of a Polygon

The formula to find the measure of each exterior angle of a polygon is given by:

Each Exterior Angle = 360 / n degrees

Examples of Polygons

Some examples of polygons include:

Triangle: A 3-sided polygon
Square: A 4-sided regular polygon
Pentagon: A 5-sided polygon
Hexagon: A 6-sided polygon
Octagon: An 8-sided polygon

Conclusion

Understanding the properties and characteristics of polygons is important for various areas of mathematics, including geometry and trigonometry. Knowing the types of polygons and their properties can help in solving problems related to shapes and measurements.

◂Math Worksheets and Study Guides Sixth Grade. Area of Coordinate Polygons

Study Guide

Area of Coordinate Polygons

Activity Lesson

Area of Coordinate Polygons

Worksheet/Answer key

Area of Coordinate Polygons

Worksheet/Answer key

Area of Coordinate Polygons

Worksheet/Answer key

Area of Coordinate Polygons

The resources above cover the following skills:

Geometry (NCTM)

Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

Use coordinate geometry to represent and examine the properties of geometric shapes.

Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides.

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

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

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

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Connections to the Grade 6 Focal Points (NCTM)

Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.