Question

The figure is the net for rectangular prism. What is the surface area of the rectangular prism represented by the net?_mm

Answer 1

We will ave the following:

First, we can see that the area of certain segments is the same [each face has an equal image], now we will have to determine the area of each one of those faces, eaxcept for the copies, that is:

`\begin{cases}_{}A_1=(11mm)(5mm) \\ \\ A_2=(11mm)(4mm) \\ \\ A_3=(5mm)(4mm)\end{cases}\Rightarrow\begin{cases}A_1=55mm^2 \\ \\ A_2=44mm^2 \\ \\ A_3=20mm^2\end{cases}`

Now, we will then have that the total surface are is given by:

`A_T=2A_1+2A_2+2A_3\Rightarrow A_T=2(A_1+A_2+A_3)`

So, now we simply replace and solve for AT, that is:

`A_T=2(55mm^2+44mm^2+20mm^2)\Rightarrow A_T=2(119mm^2)`
`\Rightarrow A_T=238mm^2`

So, the total surface are is 338 mm^2.