Rectangular Prisms

A rectangular prism is a three-dimensional shape that has six faces, all of which are rectangles. It is also known as a cuboid. The opposite faces of a rectangular prism are equal in size and shape. The rectangular prism is a special case of a parallelepiped, which is a six-faced figure with each pair of opposite faces being identical rectangles.

Properties of Rectangular Prisms

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

2. Edges: A rectangular prism has 12 edges, where three edges meet at each vertex.

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

4. Diagonals: The rectangular prism has 4 space diagonals that connect opposite vertices.

5. Volume: The volume of a rectangular prism can be 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 surface area of a rectangular prism can be calculated using the formula SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism.

Example Problem:

Find the volume and surface area of a rectangular prism with length 5 cm, width 3 cm, and height 4 cm.

Volume: V = l × w × h = 5 cm × 3 cm × 4 cm = 60 cubic cm

Surface Area: SA = 2lw + 2lh + 2wh = 2(5 cm × 3 cm) + 2(5 cm × 4 cm) + 2(3 cm × 4 cm) = 30 + 40 + 24 = 94 square cm

Study Guide:

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

1. Identifying the properties of a rectangular prism (faces, edges, vertices, and diagonals).
2. Understanding how to calculate the volume and surface area using the appropriate formulas.
3. Practicing solving problems involving rectangular prisms in real-life situations.
4. Recognizing the relationships between the dimensions (length, width, and height) of a rectangular prism and its volume and surface area.
5. Applying the concepts of rectangular prisms to solve word problems and geometric problems.

By mastering these concepts and skills, you can confidently work with rectangular prisms and solve a variety of problems related to their volume and surface area.