Octagon Study Guide

An octagon is a polygon with eight sides and eight angles. It is a two-dimensional shape that is commonly found in architecture, design, and nature.

Properties of an Octagon:

1. Number of Sides: An octagon has 8 sides.

2. Number of Angles: An octagon has 8 angles.

3. Sum of Interior Angles: The sum of the interior angles of an octagon is 1080 degrees.

4. Sum of Exterior Angles: The sum of the exterior angles of an octagon is 360 degrees.

5. Regular vs Irregular Octagon: A regular octagon has all its sides and angles equal, while an irregular octagon has sides and/or angles of different lengths and measures.

Formulas for Octagon:

1. Perimeter of an Octagon: If the length of each side of the octagon is equal to 'a', then the perimeter, P, of the octagon is given by the formula: P = 8a.

2. Area of an Octagon: The area, A, of a regular octagon with side length 'a' can be calculated using the formula: A = 2(1 + √2)a².

Examples of Octagon:

Here are some examples of objects that can be represented by an octagon:

Stop signs
Regular stop sign
Regular nut
Regular bolt head
Regular washer

Now that you understand the properties and formulas related to octagons, you can practice solving problems involving octagons to reinforce your understanding.

◂Math Worksheets and Study Guides Sixth Grade. Area

The resources above cover the following skills:

Geometry (NCTM)

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.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

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.