Key takeaway: A rectangular prism is a solid with six rectangular faces, twelve edges and eight vertices, where opposite faces are identical, like a shoebox or a brick.
Grade 66.G.A.2Geometry and Measurement
Definition of Rectangular Prism
A rectangular prism is a box-shaped solid made of six flat rectangles. Its faces meet at right angles along twelve straight edges, and the edges meet at eight corner points called vertices.
Opposite faces match in size and shape, so you only need three different rectangles to describe all six. The three side lengths, called length, width and height, tell everything about the size of the solid. When all three are equal, the prism is a cube. Shoeboxes, cereal boxes and bricks are everyday examples. In some books, the term cuboid is used.
Formula and notation
Dimensions are given as length, width and height:
\[\ell \times w \times h = 13 \times 8 \times 5\]
The edges come in three groups of four, so the total edge length is \(4(\ell + w + h)\). The volume is \(\ell w h\), and the surface area is \(2(\ell w + \ell h + w h)\).
Key facts
- It has 6 faces, 12 edges and 8 vertices.
- Each face is a rectangle, and opposite faces are congruent.
- A cube is the special case with three equal dimensions.
- Cutting along edges and unfolding the surface gives a net of six rectangles.
Rectangular Prism example
A shoebox is 13 inches long, 8 inches wide and 5 inches tall. Gift ribbon is run along every edge. How much ribbon is needed, and what is the volume of the box?
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The 12 edges form 4 lengths, 4 widths and 4 heights.
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Total edge length: \(4(13 + 8 + 5) = 4 \times 26 = 104\) inches.
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Volume: \(13 \times 8 \times 5 = 520\) cubic inches.
The box needs 104 inches of ribbon and has a volume of 520 cubic inches.
Common mistake
Watch out
Luis says a rectangular prism has 12 vertices because “it has 12 edges.”
Why it is wrong
Edges and vertices are different parts. Edges are the segments, and there are 12. Vertices are the corner points where three edges meet, and there are 8. Check with a cube: 4 corners on top plus 4 on the bottom.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Geometry and Measurement