Rectangular Prism
In short: Rectangular prism names the box-shaped solid whose six faces are all rectangles, such as a cereal box, described by its length, width and height.
6th GradeGeometry6.G.A.2
What is Rectangular Prism?
A shoebox, a brick and a refrigerator are all shaped like a rectangular prism. Every face is a rectangle, opposite faces are identical, and any two faces that touch meet at a right angle.
Counting parts gives 6 faces, 12 edges and 8 vertices. Its three dimensions \(\ell\), \(w\) and \(h\) control everything: volume is \(V = \ell w h\) and outside area is \(2(\ell w + \ell h + w h)\). Make all three equal and you get a cube.
How to spot it
- A figure has six flat rectangular faces that meet at corners like a box.
- A problem gives three measurements: length, width and height.
- A question counts faces, edges or corners of a package, room or container.
- A net unfolds into six rectangles, with matching pairs.
The method
- Name the three dimensions and make sure they use the same unit.
- For capacity, multiply them: \(V = \ell w h\).
- For the outside covering, add the areas of the three different faces and double the total.
- For a frame of edges, add the three dimensions and multiply by 4.
Rectangular Prism: solved example
Problem
A furniture maker in Asheville builds a wooden frame in the shape of a rectangular prism, with edges of 30 cm, 20 cm and 15 cm. How much wood is needed for all 12 edges, and how much room is there inside it?
Solution
Four edges have each length, so the wood is \(4(30 + 20 + 15) = 4 \cdot 65 = 260\) cm.
The space inside is \(30 \cdot 20 \cdot 15 = 9{,}000\) cubic centimeters. So the frame needs 260 cm of wood and encloses 9,000 cm³.
Try it
Question 1
How many edges of a prism have the same length as its height?
Show the answer
Four, because the four vertical edges are all parallel and equal.
Question 2
A jewelry case measures 9 in., 6 in. and 2 in. along its edges. How many cubic inches does it hold?
Show the answer
\(9 \cdot 6 \cdot 2 = 108\) cubic inches.
Rectangular Prism vs. Volume
The prism is the solid shape. Volume is a number describing how much space that shape holds. A given prism has one volume, but many different prisms can share the same volume, such as 4 by 6 by 5 and 2 by 3 by 20.
Keep going
Lessons
Worksheets and quizzes
- Volume of Prisms with Fractional Edges – Worksheet
- Volume of Prisms with Fractional Edges – Quiz
- Nets and Surface Area – Worksheet
- Nets and Surface Area – Quiz
Related words
Whole dictionary: A–Z · 6th Grade · Geometry