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.

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.

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.

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.

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.

.Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

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

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.