Question

The net of a rectangular prism is shown below. The surface area of each is labeled

Answer 1

Given:

Area of box I = 48 cm²

Area of box 2 = 24 cm²

Area of box 3 = 48 cm²

Area of box 4 = 24 cm²

Area of box 5 = 72 cm²

Area of box 6 = 72 cm²

• Let's find the values which represent the dimensions of the prism.

Let L represent the length.

Let w represent the width

Let h represent the height.

Now, to find the surface area of a rectangular prism apply the formula:

A = 2(wL + Lh + wh)

Now, given each rectangular face, we have:

Area of length and width, Lw = 72 cm²

Area of length and height, Lh = 48 cm²

Area of width and height, wh = 24 cm²

Now to find the dimensions, we have:

`\begin{gathered} (Lh)/(wh)=(48)/(24) \\ \\ (L)/(w)=2 \\ \\ L=2w \end{gathered}`

Now, substitute 2w for L in Lw:

`\begin{gathered} Lw=72 \\ \\ 2w(w)=72 \\ \\ 2w^2=72 \\ \\ w^2=(72)/(2) \\ \\ w^2=36 \\ \\ \text{ take the square root of both sides:} \\ √(w^2)=√(36) \\ \\ w=6 \end{gathered}`

Therefore, the width is 6 cm.

Now, substitute 6 for w in wh:

`\begin{gathered} wh=24 \\ \\ 6*h=24 \\ \\ Divide\text{ both terms by:} \\ (6*h)/(6)=(24)/(6) \\ \\ h=4 \end{gathered}`

Now, substitute 4 for h in Lh:

`\begin{gathered} Lh=48 \\ \\ L*4=48 \\ \\ \text{ Divide both sides by 4:} \\ (L*4)/(4)=(48)/(4) \\ \\ L=12 \end{gathered}`

Therefore, the values which represent the dimensions are:

4, 6, 12

ANSWER:

4, 6, 12