A rectangle is a quadrilateral with four right angles. This means that opposite sides of a rectangle are equal in length and parallel to each other. It is a special case of a parallelogram where all angles are right angles.

**Four Right Angles:**All angles in a rectangle are right angles, meaning they measure 90 degrees.**Opposite Sides are Equal:**The opposite sides of a rectangle are equal in length.**Diagonals are Equal:**The diagonals of a rectangle are equal in length and bisect each other.**Area and Perimeter:**The area of a rectangle is given by the formula: A = length x width, and the perimeter is given by: P = 2(length + width).

Area of a Rectangle: A = length x width

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

1. Find the area and perimeter of a rectangle with length = 5 cm and width = 8 cm.

**Area:** A = 5 cm x 8 cm = 40 square cm

**Perimeter:** P = 2(5 cm + 8 cm) = 26 cm

2. If the perimeter of a rectangle is 30 meters and its length is 10 meters, find the width of the rectangle.

Let the width be represented by 'w'.

30 = 2(10 + w)

30 = 20 + 2w

2w = 30 - 20

2w = 10

w = 5 meters

- Find the area of a rectangle with length = 12 cm and width = 6 cm.
- If the area of a rectangle is 56 square units and its length is 8 units, find the width of the rectangle.
- A rectangle has a perimeter of 24 meters and its width is 5 meters. Find the length of the rectangle.

Rectangles are important geometric shapes with various properties and formulas for area and perimeter. Understanding these concepts is crucial for solving problems related to rectangles.

Study GuideGeometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key Numerical & Geometric Proportions

Number and Operations (NCTM)

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.

Measurement (NCTM)

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

Solve problems involving scale factors, using ratio and proportion.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.