Question

identifying three - dimensional solids
what three - dimensional solid has 6 rectangular faces, 2 equal bases that are not rectangles, and 18 edges?
triangular prism
pentagonal prism
hexagonal prism
octagonal prism

Explanation:

Step1: Recall prism - face and edge properties

A prism has two congruent bases and rectangular lateral - faces. The number of edges $E$, faces $F$, and vertices $V$ of a polyhedron satisfy Euler's formula $F + V=E + 2$. Also, if the base of a prism has $n$ sides, the number of rectangular faces is $n$, and the number of edges $E = 3n$.

Step2: Analyze the number of rectangular faces

We are given that the number of rectangular faces is 6. In a prism, the number of rectangular faces is equal to the number of sides of the base polygon. So, if the number of rectangular faces $n = 6$, the base is a hexagon.

Step3: Analyze the number of edges

We know that for a prism with a base having $n$ sides, the number of edges $E=3n$. Given $E = 18$, then $3n=18$, which gives $n = 6$. A prism with a hexagonal base is a hexagonal prism.

Answer:

hexagonal prism