This figure represents a large storage container that will be built out of a new durable material. The storage company needs 8 o

Question

3 years ago

14

This figure represents a large storage container that will be built out of a new durable material. The storage company needs 8 o

f these containers.
How much of the new material is needed to build all 8 containers?

Enter your answer in the box.

ft²
Right pentagonal prism. The height of the prism is 8 ft. The base has two pairs of parallel sides. The sides are consecutively labeled 5 ft, 3 ft, 5 ft, 2 ft, and 7 ft. The parallel sides are those labeled 3 ft and 7 ft, and 5 ft and 2 ft.

Mathematics

1 answer:

zepelin [54] · Answer 1 · 2023-01-03T16:21:55+03:00

The amount of material needed for the containers is its surface area

The amount of material needed for the 8 containers using the assumed parameters is 3080 square feet

<h3>How to determine the amount of material?</h3>

The question is incomplete, as the figure of the right pentagonal prism is not given.

So, I will provide a general explanation.

The surface area (SA) of a right pentagonal prism is:

SA = 5b(a + h)

Where:

b represents the base length
a represents the apothem
h represents the height

From the question, we have the height of the prism to be 8 ft.

Assume that:

a = 3 ft and b = 7 ft

The equation becomes

SA = 5 * 7 * (3 + 8)

Evaluate the product

SA = 385

The amount of material needed for the 8 containers would be:

Amount = 8 * 385 square feet

Amount = 3080 square feet

Hence, the amount of material needed for the 8 containers using the assumed parameters is 3080 square feet