A rectangle is a four-sided polygon with opposite sides that are equal in length and all interior angles are 90 degrees.

1. Opposite sides of a rectangle are equal in length.

2. The diagonals of a rectangle are equal in length and bisect each other.

3. The area of a rectangle is given by the formula: A = length x width.

4. The perimeter of a rectangle is given by the formula: P = 2(length + width).

Area of a Rectangle: A = length x width

Perimeter of a Rectangle: P = 2(length + width)

**Example 1:** Find the area of a rectangle with a length of 5 units and a width of 8 units.

**Solution:** A = 5 x 8 = 40 square units

**Example 2:** Find the perimeter of a rectangle with a length of 12 units and a width of 6 units.

**Solution:** P = 2(12 + 6) = 2(18) = 36 units

- Calculate the area of a rectangle with a length of 10 units and a width of 4 units.
- Find the perimeter of a rectangle with a length of 15 units and a width of 7 units.
- If the area of a rectangle is 48 square units and the length is 8 units, what is the width?

Now you can use the formulas and properties of rectangles to solve problems and apply them in real-life situations. Good luck with your studies!

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.