If a base of a prism has n sides, which provides s(n), the number of surfaces the prism has?

Question

If a base of a prism has n sides, which provides s(n), the number of surfaces the prism has?

A. s(n) = n +1

B. s(n)= n+2

C. 2n+1

D. 2n+2

Is the anwser A?, Because when I put in 5,6, and 7 into the equation it equal the next shapes surface

Answer 1

So this question wants you to find an equation relating the number of sides in the base of the prism to the total number of surfaces of the prism. To tackle this, let's start with the first prism where the base is a triangle. Let me ask now, how many sides does a triangle have? It has 3. Therefore the base of the first prism, which is a triangle, has 3 sides. How many surfaces does the first prism have? It has 5. So a prism with 3 sides in the base has 5 surfaces.

Now let's move on to the other prisms. The second prism has a base of a quadrilateral. A quadrilateral has 4 sides. The second prism has 6 surfaces. So a prism with 4 sides in the base has 6 surfaces. A pattern is now emerging. We see that the amount of surfaces seems to be the number of sides in the base + 2.

Let's check the third prism. The third prism has a base of a pentagon. A pentagon has 5 sides. The third prism has 7 surfaces. The pattern holds. The amount of surfaces in the prism is the number of sides in the base + 2.

B is the answer.