Question

the right hexagonal prism shown to the right has regular hexagons as bases.
a. name all the pairs of parallel lateral faces. (faces are parallel if the planes containing the faces are parallel.)
b. what is the measure of the dihedral angle between two adjacent lateral faces? why?
a. choose the correct answer below
a. the following faces are parallel
quadrilaterals affa and dccd
quadrilaterals baab and edde
quadrilaterals cbbc and feef
b. the following faces are parallel
quadrilaterals affa and edde
quadrilaterals baab and cbbc
quadrilaterals dccd and feef
c. the following faces are parallel
quadrilaterals affa and feef
quadrilaterals baab and edde
quadrilaterals cbbc and dccd
d. the following faces are parallel
quadrilaterals affa and baab
quadrilaterals cbbc and dccd
quadrilaterals edde and feef

Explanation:

Step1: Recall properties of a right - hexagonal prism

In a right - hexagonal prism with regular hexagons as bases, opposite lateral faces are parallel.

Step2: Identify parallel lateral faces

The pairs of parallel lateral faces are: quadrilaterals AFF'A' and DCC'D'; quadrilaterals BAA'B' and EDD'E'; quadrilaterals CBB'C' and FEE'F'.

Answer:

A. The following faces are parallel: quadrilaterals AFF'A' and DCC'D'; quadrilaterals BAA'B' and EDD'E'; quadrilaterals CBB'C' and FEE'F'