Hexagon

A hexagon is a polygon with six sides and six angles. The sum of the interior angles of a hexagon is always 720 degrees. Each interior angle of a regular hexagon measures 120 degrees.

Types of Hexagons

1. Regular Hexagon: A hexagon with all sides and angles congruent.

2. Irregular Hexagon: A hexagon with sides and/or angles that are not congruent.

3. Convex Hexagon: A hexagon in which all of its interior angles are less than 180 degrees.

4. Concave Hexagon: A hexagon in which at least one of its interior angles is greater than 180 degrees.

Formulas and Properties

1. The sum of the interior angles of a hexagon with n sides is given by the formula: (n-2) * 180 degrees. For a hexagon, n = 6, so the sum of its interior angles is (6-2) * 180 = 4 * 180 = 720 degrees.

2. The measure of each interior angle of a regular hexagon is given by the formula: 180 * (n-2) / n, where n is the number of sides. For a hexagon, the measure of each interior angle is 180 * (6-2) / 6 = 180 * 4 / 6 = 120 degrees.

3. The perimeter of a hexagon is the sum of the lengths of its six sides.

4. The area of a regular hexagon can be calculated using the formula: (3√3 * s^2) / 2, where s is the length of a side.

Example Problems

1. Find the measure of each interior angle of a regular hexagon.

Answer: Using the formula, the measure of each interior angle is 180 * (6-2) / 6 = 120 degrees.

2. Calculate the area of a regular hexagon with a side length of 8 cm.

Answer: Using the area formula, the area is (3√3 * 8^2) / 2 = (3√3 * 64) / 2 = 96√3 square cm.

Study Guide

When studying hexagons, it's important to understand the properties and formulas associated with this type of polygon. Practice calculating the interior angles, perimeter, and area of hexagons, both regular and irregular. Familiarize yourself with the difference between convex and concave hexagons, and be able to identify and classify them. Additionally, work on problem-solving skills by solving various example problems related to hexagons.

Remember, practice is key to mastering the concept of hexagons. Work through different types of problems and seek help if you encounter any difficulties.

◂Math Worksheets and Study Guides Eighth Grade. Collecting and describing data

Study Guide

Collecting and describing data

Worksheet/Answer key

Collecting and describing data

Worksheet/Answer key

Collecting and describing data

Worksheet/Answer key

Collecting and describing data

The resources above cover the following skills:

Data Analysis and Probability (NCTM)

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.

Select and use appropriate statistical methods to analyze data.

Find, use, and interpret measures of center and spread, including mean and interquartile range.

Develop and evaluate inferences and predictions that are based on data.

Use conjectures to formulate new questions and plan new studies to answer them.

Grade 8 Curriculum Focal Points (NCTM)

Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets

Students use descriptive statistics, including mean, median, and range, to summarize and compare data sets, and they organize and display data to pose and answer questions. They compare the information provided by the mean and the median and investigate the different effects that changes in data values have on these measures of center. They understand that a measure of center alone does not thoroughly describe a data set because very different data sets can share the same measure of center. Students select the mean or the median as the appropriate measure of center for a given purpose.

Connections to the Grade 8 Focal Points (NCTM)

Data Analysis: Building on their work in previous grades to organize and display data to pose and answer questions, students now see numerical data as an aggregate, which they can often summarize with one or several numbers. In addition to the median, students determine the 25th and 75th percentiles (1st and 3rd quartiles) to obtain information about the spread of data. They may use box-and-whisker plots to convey this information. Students make scatterplots to display bivariate data, and they informally estimate lines of best fit to make and test conjectures.