What Is a Rectangular Prism?
A rectangular prism is a solid, three-dimensional shape with six flat faces shaped like rectangles. A small shipping box is a familiar example. It has length, width, and height, so it takes up space. A flat rectangle on a page is different: it has only two dimensions.
The word prism names a solid shape with the same cross-section from one end to the other. In the box-shaped rectangular prism taught in elementary school, the faces meet at right angles.
How to Spot One: Faces, Edges, and Corners
You can identify a rectangular prism by looking closely at its surfaces and where they meet.
•Faces are the flat surfaces. A rectangular prism has 6 faces: a top, a bottom, a front, a back, and two sides. A square face counts because every square is also a rectangle.
•Edges are the straight line segments where two faces meet. A box has 4 edges around the top, 4 around the bottom, and 4 joining the top to the bottom. That makes 12 edges.
•Vertices are the corners where edges meet. A box has 4 corners on top and 4 on the bottom, for 8 vertices. One corner is a vertex. More than one are vertices.
If you are looking at a drawing, some edges may look slanted because the artist shows the box in perspective. The real shape still has rectangular faces and square corners.
Is a Cube a Rectangular Prism?
Yes. A cube is a special kind of rectangular prism. A cube has six square faces and all its edges have the same length. Since a square is a rectangle, a cube fits the definition of a rectangular prism.
Not every rectangular prism is a cube. A book-shaped box, for example, can have long, short, and tall edges of different lengths. Its faces remain rectangles, but they are not all squares.
Rectangular Prisms Around You
Look for rectangular prisms in objects such as a book, a brick, a tissue box, or a package. These everyday objects are close to the geometric shape, even if their corners are rounded or their surfaces are not perfectly flat. In geometry, the ideal shape has flat rectangular faces and straight edges.
Try a Quick Box Check
Find a small box. Point to one flat face, then trace an edge with your finger and touch a corner. Turn the box and count the faces, edges, and corners. Can you explain why a square face still fits the shape?
Quick Practice
A student says a cube is not a rectangular prism because its faces are squares. Is the student right? Explain your answer.
Answer: No. Every square is also a rectangle, so the cube has six rectangular faces and meets the definition of a rectangular prism.
Related Terms
Explore cube, 3D shape, face, edge, vertex, rectangle, and volume. In Grade 5, students use unit cubes and multiplication to find the volume of right rectangular prisms, as described in Common Core standard 5.MD.C.
Frequently Asked Questions
What is another name for a rectangular prism?
Cuboid is another name used for a rectangular prism. In US elementary lessons, rectangular prism is common.
Do all six faces have to be different sizes?
No. Opposite faces match in size. Some or all faces may be squares, as they are on a cube.
How is a rectangular prism different from a triangular prism?
A rectangular prism has rectangular faces. A triangular prism has two triangular bases and three rectangular side faces.