Dodecahedron

A dodecahedron is a three-dimensional shape that has 12 pentagonal faces, 20 vertices, and 30 edges. Each face of a dodecahedron is a regular pentagon, which means all the sides and angles of the pentagon are equal.

Dodecahedron Formulae

To calculate the surface area (A) of a dodecahedron, you can use the formula:

A = 3√25 + 10√5 * s^2

Where s is the length of the side of the pentagon.

To find the volume (V) of a dodecahedron, you can use the formula:

V = (15 + 7√5) / 4 * s^3

Where s is the length of the side of the pentagon.

Properties of a Dodecahedron

Some key properties of a dodecahedron include:

It has 12 faces, each of which is a regular pentagon.
It has 20 vertices where three faces meet.
It has 30 edges, where the faces meet.
It is a regular convex polyhedron.
It is one of the five platonic solids.

Study Guide

When studying dodecahedrons, it's important to understand the following concepts:

Identifying the faces, edges, and vertices of a dodecahedron.
Calculating the surface area and volume of a dodecahedron using the formulas provided.
Understanding the properties of a dodecahedron, such as being a regular convex polyhedron and one of the five platonic solids.
Recognizing real-life objects that have a dodecahedral shape, such as soccer balls and certain viruses.

Knowing these concepts will help you understand and apply the principles of dodecahedrons in various mathematical problems and real-world scenarios.

◂Math Worksheets and Study Guides Eighth Grade. Real numbers

The resources above cover the following skills:

The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. [8-NS1]

Expressions and Equations

Work with radicals and integer exponents.

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. [8-EE2]