Middle School

Pentagonal prism B is the image of pentagonal prism A after dilation by a scale factor of 55. If the surface area of pentagonal prism B is 3425 km\(^2\), find the surface area of pentagonal prism A, the preimage.

Answer :

Answer:

137 km^2

Step-by-step explanation:

prism A: scale factor 5

surface area of B: 3425 km

what is prism A's surface area?

well first of all, pre image is prism A, NOT prism B. prism A is smaller than B.

so, 3425 is not going to get multiplied by 5.

3425 = x times 5^2

3425 = x times 25

3425 25x

____ = ____

25 25

137 = x

x = 137

Scale factors are used to enlarge or compress the surface area of a shape

The surface area of pentagonal prism A is 129.8 km^2

How to determine the surface area of prism A

The area of prism B is given as:

[tex]Area = 3425km^2[/tex]

The scale factor from A to B is:

[tex]k = 5[/tex]

The area of shape A is then calculated as:

[tex]A = \frac{Area\ of\ B}{k^2}[/tex]

So, we have:

[tex]A = \frac{3245}{5^2}[/tex]

[tex]A = 129.8[/tex]

Hence, the surface area of pentagonal prism A is 129.8 km^2

Read more about scale factors at:

https://brainly.com/question/3457976

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