A state department of education, as a question on the public-release form of a statewide standardized test, released a question to the public in which students have to choose the correct value, from a list of four, for the surface area of a rectangular prism whose length, width, and height are given.
There’s a diagram, and it looks something like this:
Unfortunately, the formula for surface area is not on the formula sheet provided by the state for this particular test. Therefore, we’re going to have to figure it out (if we don’t have it memorized).
To start with, a rectangular prism has six faces. The total surface area is just the area of each of those faces added up. And we know each face is a rectangle.
The formula for the area of a rectangle, of course, is length × width. Multiplying the two sides of each face by each other will give us the area for that face.
In this cube, the two bases (3 feet by 3 feet) have an area of 9 square feet. That makes 18 square feet for the two bases, which are actually squares in this case.
Next, each of the sides has a length of 15 feet and a width of 3 feet. Multiplying those gives us 45 square feet for each face on the side of the rectangular prism.
There are four of those faces, so 45 × 4 = 180.
Adding that to the 18 square feet we got for the combined areas of the two bases, we find that the total surface area of this rectangular prism is 198 square feet.
And finally, if you would like more practice on surface area problems, visit our online library at VoxLearn.org and search for “surface area.”