Question

The pentagonal prism below has a base area of 39.1 units2 and a volume of 273.7 units3 . Find its height.

Answer 1

The calculated height of the pentagonal prism is 7 units

How to determine the height of the pentagonal prism

From the question, we have the following parameters that can be used in our computation:

Volume = 273.7 cubic units

Base area = 39.1 square units

The volume of a pentagonal prism is given by the formula:

Volume = Base area * Height

So, we have

Height = Volume/Base area

Substitute the known values into the equation

Height = 273.7/39.1

Evaluate

Height = 7

Hence, the height of the pentagonal prism is 7 units

Answer 2

Given:

The base area of the pentagonal prism

`=39.1\text{ units}^2.`

The volume of the pentagonal prism

`=273.7\text{ units}^3.`

Required:

We have to find the height.

Step-by-step explanation:

The formula for the volume of the pentagonal prism is

`(5)/(2)*\text{ area of base}*\text{ height.}`

Therefore, we can equate the given volume with the above formula.

Then proceed as follows:

`\begin{gathered} (5)/(2)*\text{ area of base}*\text{ height}=273.7 \\ \Rightarrow(5)/(2)*39.1*\text{ height}=273.7 \end{gathered}`
`\begin{gathered} \Rightarrow\text{ height}=(273.7*2)/(5*39.1) \\ \\ \Rightarrow\text{ height}=(547.4)/(195.5) \end{gathered}`
`\Rightarrow\text{ height}=2.8\text{ cm.}`

Final answer:

Hence the final answer is

`2.8\text{ cm.}`