A rectangular prism is a three-dimensional shape with six rectangular faces. It is also known as a rectangular solid or a rectangular box. The faces of a rectangular prism are all rectangles, and opposite faces are congruent and parallel.

Properties of Rectangular Prism

1. Faces: A rectangular prism has 6 faces, all of which are rectangles.

2. Edges: It has 12 edges, where each edge is the meeting of two faces.

3. Vertices: A rectangular prism has 8 vertices, where three edges meet.

4. Diagonals: The rectangular prism has 4 space diagonals, connecting opposite vertices.

5. Volume: The volume of a rectangular prism is calculated using the formula: V = l * w * h, where l is the length, w is the width, and h is the height of the prism.

6. Surface Area: The total surface area of a rectangular prism is given by the formula: 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height of the prism, respectively.

Example Problems

1. Calculate the volume of a rectangular prism with length 5 cm, width 3 cm, and height 4 cm.

Volume (V) = l * w * h = 5 * 3 * 4 = 60 cubic cm

2. Find the surface area of a rectangular prism with length 6 m, width 4 m, and height 2 m.

Surface Area = 2lw + 2lh + 2wh = 2(6*4) + 2(6*2) + 2(4*2) = 88 square meters

Study Guide

When studying rectangular prisms, make sure to focus on the following key points:

Understanding the properties of a rectangular prism, including its faces, edges, and vertices.
Mastering the formulas for calculating the volume and surface area of a rectangular prism.
Practicing solving problems involving rectangular prisms, such as finding the volume, surface area, or dimensions.

Remember to visualize the rectangular prism in different orientations to better understand its properties and relationships between its dimensions.

Good luck with your studies!

◂Math Worksheets and Study Guides Seventh Grade. Measurement, Perimeter, and Circumference

Study Guide

Measurement, Perimeter, and Circumference

Worksheet/Answer key

Measurement, Perimeter, and Circumference

Worksheet/Answer key

Measurement, Perimeter, and Circumference

Worksheet/Answer key

Measurement, Perimeter, and Circumference

The resources above cover the following skills:

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

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

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

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.