Question

The cross section of a prism has x sides.

Select the expression for the number of edges of the prism.
DX
A
2x
B
3x
C
x + 4
D

Answer 1

E = 2(3x) = 6x

Explanation:

To find the number of edges of a prism, we can use the formula E = (2n), where E is the number of edges and n is the number of vertices.

For a prism, we know that it has two identical polygonal faces (the bases), each with x sides. Each of these faces will have x vertices since each vertex is where two sides meet. The other vertices of the prism will be where the lateral faces meet the bases, which is equal to x for each base. Therefore, the total number of vertices in the prism is 2x + x = 3x.

Using the formula E = (2n), we can find the number of edges of the prism:

E = 2(3x) = 6x

Therefore, the expression for the number of edges of the prism is 6x, which is not listed as an option. The closest option is B, 3x, but that represents the number of edges of a triangular prism, not a prism with x sides.

Answer 2

The total number of edges is 3x. Option C

Each base of the prism contributes x edges (since a polygon with x sides has x edges). Therefore, both bases together contribute 2x edges.

Each side of the prism connects the corresponding sides of the two bases. As there are x sides in the cross-section, each side contributes 1 edge to the prism.

So, the total number of edges in the prism can be calculated as the sum of edges from the bases and the sides:

Total edges = Edges from bases + Edges from sides

Total edges = 2x (from bases) + x (from sides)

Total edges = 2x + x = 3x