Question

A pentagonal prism has 7 faces. How many vertices does it have?
A. 15 vertices
B. 14 vertices
C. 7 vertices
D. 10 vertices

Answer 1

Hint: First of all we have to draw the figure of the pentagonal prism. A pentagonal prism has two equal bases shaped like a pentagon and it also has five faces. Later on we have to calculate the number of vertices from the figure obtained.

Complete step by step solution:
So, here before proceeding to the solution, we need to know what pentagon is and later on we have to know how it looks like.
Pentagon (Definition): A polygon with exactly 5 sides and 5 vertices is said to be pentagon.
Here we can see the figure of a pentagon.

The above figure contains exactly 5 sides and 5 vertices. So it is a pentagon.
5 sides are AB, BC, CD, DE and EA and 5 vertices are A, B, C, D and E.
Now we have to draw the figure for pentagonal Prism with exactly 7 faces.
We can see the pentagonal prism in the figure drawn below.

Here the above figure contain 7 faces i.e. ABIHG, BICD, IHED, GHEF, FGAJ, ABCJ and CDEFJ
These are the 7 faces and now we have to find the total number of vertices of this pentagonal prism with 7 faces.
So, the vertices are A, B, C, D, E, F, G, H, I, and J
So, here the total number of vertices is 10.
So the answer is option (D).

Note: Students may have the chances of making mistakes while drawing the figure of pentagonal prism with exactly 7 sides and while counting the vertices, you can count the vertices of faces ABIHG and CDEFJ i.e. upper and lower face for simplicity. So, we can avoid mistakes while counting the total number of vertices.