Question

Previous Answer: 12877 Things to consider! • What are the solid/solids of the figure? • What are you being asked to find? • What are you being given? Find the Volume 6 ft 4 ft 4 ft 12 ft 6 ft

Answer 1

Answer: Total Volume = Rectangular Prism Volume + Triangular Prism Volume

Total Volume = 288 + 72 =360 cubic-feet

Step by step solution:

Let's start with the things we need to consider:

• In the figure, we have 2 solids: A triangular prism and a rectangular prism

,

• We are being asked to find the volume of the solids.

• We are being given the sides of the rectangle (rectangle base and rectangle height) and the height of the prism. For the triangular prism, we have the triangle base, triangle height, and prism height.

The volume of the rectangular prism is:

`\begin{gathered} V=\text{Arectangle}\cdot\text{height prism} \\ V=(\text{rectangle base }\cdot\text{ rectangle height)}\cdot height\text{ prism} \end{gathered}`

Rectangle base = 12

Rectangle height = 6

Prism height = 4

We plug in these values on the formula to find the volume of the rectangular prism:

`\begin{gathered} V=(12\cdot6)\cdot4 \\ V=72\cdot4=288ft^3 \end{gathered}`

The volume of the triangular prism is:

`\begin{gathered} V=\text{Atriangle}\cdot\text{height prism} \\ V=(\frac{triangle\text{ base}}{2}\cdot\text{triangle height})\cdot height\text{ prism} \end{gathered}`

Triangle base = 6

Triangle height = 4

Prism height = 6

We plug in these values on the formula to find the volume of the triangular prism:

`\begin{gathered} V=((6)/(2)\cdot4)\cdot6 \\ V=12\cdot6=72ft^3 \end{gathered}`

Total Volume = Rectangular Prism Volume + Triangular Prism Volume

Total Volume = 288 + 72 =360 cubic-feet