Question

Can someone help me with this geometry question? First box has 3 options: 60,96,48Second box has two options: 480 and 552Third box: 180 and 216

Answer 1

Surface area of a square prism is:

`\begin{gathered} \text{4\lparen ah\rparen= SA square prism} \\ 4(20)(6)\text{= SA square prism} \\ 80(6)\text{= SA square prism} \\ 480=\text{SA square prism} \\ \\ \end{gathered}`

The surface area of the square prism 480.

The surface area for the cube is:

`\begin{gathered} 5a^2=\text{ SA cube} \\ 5(6)^2=\text{ SA cube} \\ 5(36)=\text{ SA cube} \\ 180=\text{ Surface area of the cube} \end{gathered}`

The surface area of the cube is: 180.

The surface area of the pyramid is:

`\begin{gathered} SurfaceAreaPyramid=4bh \\ SAPyramid=\text{4\lparen6\rparen\lparen4\rparen} \\ SAPyramid=\text{ 96} \\ \end{gathered}`

The surface area of the pyramid i 96.

In each geometric figure, we have to remove the inner square faces, since they are not on the surface.

The total surface area is:

`\begin{gathered} SA\text{ cube + SA square prism + SA pyramid= Total SA} \\ 180\text{ + 480 + 96= Total SA} \\ 756=\text{ Total surface area. } \end{gathered}`

The total surface area is 756.