Pentagonal prism B is the image of pentagonal prism A after dilation by a scale factor of [tex]\frac{1}{5}[/tex]. If the surface area of pentagonal prism B is [tex]5 \text{ cm}^2[/tex], find the surface area of pentagonal prism A, the preimage.

Pentagonal prism B is the image of pentagonal prism A after dilation by a scale factor of 1/5. If the surface area of pentagonal prism A is 25 in2, find the surface area of pentagonal prism B, the image.

^im pretty sure that's what your question says, it's what mine says.

B is the image of A

B is scale factor 1/5

surface area of A is 25in2

what is surface area of B?

A times b2

25 times 1/5^2

25 times 1/25 (because 1/5^2 is 1/25) (you can also use 0.04 for this)

1

answer is 1 inch

MrRoyal MrRoyal · Answer 2 · 2025-03-23T00:46:32-04:00

Both prisms would have different areas, and the surface area of the pentagonal prism A, the preimage is 125 cm^2

How to determine the surface area of the prism A?

The given parameters are:

Scale factor from A to B, k = 1/5
Surface area of B = 5

The relationship between the surface areas of both prisms is represented as:

B = A * k^2

So, we have:

5 = A * (1/5)^2

Evaluate

5 = A * 1/25

Multiply both sides by 25

A = 125

Hence, the surface area of the pentagonal prism A, the preimage is 125 cm^2