Prisms weren't invented just to divide light into beautiful rainbows; they're also useful for inducing painful headaches when you're asked to find their surface area or volume on the Praxis Core exam.
Swallow a headache tablet and try the following practice questions. In the first one, you have to find the surface area of a right rectangular prism. In the second one, you're asked to find the volume of a triangular prism.
Practice questions
- The following figure is a right rectangular prism. What is its surface area?
A. 266 m2 B. 144 m2 C. 246 m2 D. 432 m2 E. 348 m2
- A triangular prism has two triangular bases that both have an area of 19 square units. The prism has a height of 8 units. What is the volume of the prism?
A. 604 cubic units B. 76 cubic units C. 27 cubic units D. 152 cubic units E. 228 cubic units
Answers and explanations
- The correct answer is Choice (E).The surface of any right prism is Ph + 2B, which is the product of the perimeter of a base and its corresponding height, plus twice the area of the base. Any face of a right rectangular prism can be considered a base, and what you use for height must be the measure of a segment perpendicular to the face you decided to consider a base. For example, if you consider an 8 m-by-9 m face a base for the right rectangular prism in this problem, you must consider 6 m to be the height. In that case, the other 8 m-by-9 m face is also a base.
The surface area of the right rectangular prism is 348 m2.
- The correct answer is Choice (D).The volume of any prism is Bh, or base area times the height:
The volume of the prism is 152 cubic units.
