The base of a prism has \( n \) sides. a. How many lateral faces does it have? b. How many faces does it have? a. The prism has \( \square \) lateral faces. (Type an expression using n as the variable.)

To solve the problem regarding the prism with \( n \) sides, let's break it down step by step. ### a. How many lateral faces does it have? A prism is defined as a solid object with two parallel bases that are congruent polygons. The lateral faces of a prism are the faces that connect the corresponding sides of the two bases. For a prism with a base that has \( n \) sides: - Each side of the base corresponds to one lateral face. - Therefore, the number of lateral faces is equal to the number of sides of the base. Thus, the expression for the number of lateral faces is: \[ \text{Lateral Faces} = n \] ### b. How many faces does it have? The total number of faces of a prism is the sum of the lateral faces and the two bases. Since we have already established that there are \( n \) lateral faces and 2 bases, we can express the total number of faces as follows: \[ \text{Total Faces} = \text{Lateral Faces} + \text{Bases} = n + 2 \] ### Summary of Answers: - a. The prism has \( n \) lateral faces. - b. The prism has \( n + 2 \) faces.