Dodecahedron
A dodecahedron is a polyhedron with 12 flat faces, 20 vertices, and 30 edges. Each face is a regular pentagon, meaning it has five equal sides and five equal angles.
Properties of a Dodecahedron:
Surface Area and Volume:
The surface area (A) of a dodecahedron can be calculated using the formula:
A = 3 * √25 + 10 * √5 * s^2
Where s is the length of the side of the pentagon face.
The volume (V) of a dodecahedron can be calculated using the formula:
V = (15 + 7 * √5) / 4 * s^3
Where s is the length of the side of the pentagon face.
Study Guide:
- Identify the number of faces, vertices, and edges in a dodecahedron.
- Understand the concept of regular pentagon faces in a dodecahedron.
- Practice calculating the surface area and volume of a dodecahedron using the given formulas.
- Explore real-life examples of objects or structures that resemble a dodecahedron.
- Visualize and sketch a dodecahedron to understand its structure better.
Understanding the properties and calculations related to a dodecahedron can help in developing spatial reasoning and problem-solving skills.
.◂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
Activity LessonWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe 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.