What Is a Rectangular Prism?
A rectangular prism (also called a cuboid or rectangular box) is a three-dimensional solid with six rectangular faces. It has three pairs of parallel, congruent faces and is one of the most common shapes in everyday life -- from boxes and rooms to bricks and books.
Formulas for a Rectangular Prism
Volume
The amount of space enclosed inside the prism.
Surface Area
The total area of all six rectangular faces.
Space Diagonal
The longest diagonal running through the interior of the prism.
How to Calculate Rectangular Prism Properties
Volume
To find the volume, simply multiply all three dimensions together: length, width, and height. The result is expressed in cubic units. For example, if l = 5, w = 3, and h = 4, then V = 5 × 3 × 4 = 60 cubic units.
Surface Area
The surface area accounts for all six faces. There are three pairs of identical faces: top/bottom (lw), front/back (lh), and left/right (wh). Calculate each pair and double the sum: SA = 2(lw + lh + wh).
Space Diagonal
The space diagonal extends from one corner of the prism to the opposite corner, passing through the interior. It is found using the three-dimensional extension of the Pythagorean theorem: d = √(l² + w² + h²).
Real-World Applications
- Packaging: Determining box size requirements for shipping and storage.
- Construction: Computing concrete volumes for foundations and walls.
- Interior Design: Calculating room volumes for HVAC planning.
- Aquariums: Finding the water capacity of rectangular tanks.
Special Cases
When all three dimensions are equal (l = w = h), the rectangular prism becomes a cube. A cube with side length s has volume s³, surface area 6s², and space diagonal s√3.