The amount of cardboard is equal to the surface area of the prism.
We can calculate the surface area as the sum of the area of the faces.
In a rectangular prism we have 3 pairs of faces. In this case, the faces are:
- Face 1: 2 faces of dimensions 12 * 8 in.
- Face 2: 2 faces of dimensions 18 * 12 in.
- Face 3: 2 faces of dimensions 18 * 8 in.
Then, we can add the areas as:
[tex]\begin{gathered} A=2\cdot A_1+2\cdot A_2+2\cdot A_3 \\ A=2\cdot(12\cdot8)+2\cdot(18\cdot12)+2\cdot(18\cdot8) \\ A=2\cdot96+2\cdot216+2\cdot144 \\ A=192+432+288 \\ A=912\text{ in}^2 \end{gathered}[/tex]
NOTE: A1 is the area of the face 1, A2 is the area of the face 2, and A3 is the area of the face 3.
Answer: the amount of cardboard needed is 912 square inches.
