Can anyone help me to solve this, please?

A right prism has a polygonal base with n sides. Each side has a length of 5 in. The altitude of the prism is 20 in.

If the base had n+1 sides, each still having a side of length 5 in, by how much, in square inches, would the lateral area of the prism increase by? Express your answer as a number only.

I would be mighty grateful! Thanks...sz

Al = Ph = 5n * 20 = 100n in^2. = Lateral Area.

Al = Ph = (5(n+1)) * 20 = (5n+5)*20 =
(100n + 100) in^2.

Amt. Increased=(100n+100) -100n = 100 in^2.

Of course! I'd be happy to help you solve this problem.

To find the lateral area of a prism, we need to calculate the sum of the areas of all the lateral faces. In this case, since the prism is right, the lateral faces are rectangles.

The formula for finding the area of a rectangle is Length x Width. In this problem, the width will be the height of the prism, which is given as 20 inches.

Let's start by finding the lateral area of the original prism with n sides:

Lateral Area = Number of sides x Length of each side x Height

Lateral Area of the original prism = n x 5 in x 20 in

Now, let's find the lateral area of the prism with n+1 sides:

Lateral Area of the prism with n+1 sides = (n+1) x 5 in x 20 in

To find how much the lateral area increased, we need to subtract the lateral area of the original prism from the lateral area of the prism with n+1 sides:

Increase in lateral area = Lateral Area of the prism with n+1 sides - Lateral Area of the original prism

Increase in lateral area = (n+1) x 5 in x 20 in - n x 5 in x 20 in

We can simplify this expression by factoring out the common term of 100 in:

Increase in lateral area = 100 in² x ((n+1) - n)

Simplifying further:

Increase in lateral area = 100 in² x (n + 1 - n)

The n terms cancel out, leaving us:

Increase in lateral area = 100 in²

Therefore, the lateral area of the prism increases by 100 square inches when the base has n+1 sides instead of n sides.

I hope this explanation helps! Let me know if you have any further questions.