Answer :
This solid object contains 8 sides.
The side that is facing you has a surface area:
[tex]64f{ t }^{ 2 }+84f{ t }^{ 2 }=148f{ t }^{ 2 }[/tex]
The side exactly opposite this one has the same surface area - 2 sides with this surface area in total.
The bottom side has a surface area:
[tex]84f{ t }^{ 2 }[/tex]
The side to your right has a surface area:
[tex]84f{ t }^{ 2 }[/tex]
The side to your left has a surface area:
[tex]48f{ t }^{ 2 }[/tex]
The side to your top left has a surface area:
[tex]48f{ t }^{ 2 }[/tex]
The side beside the side to the top left has a surface area:
[tex]36f{ t }^{ 2 }[/tex]
The side at the very top has a surface area:
[tex]36f{ t }^{ 2 }[/tex]
Combined, the surface area is:
[tex]S=2\cdot 148f{ t }^{ 2 }+2\cdot 84f{ t }^{ 2 }+2\cdot 48f{ t }^{ 2 }+2\cdot 36f{ t }^{ 2 }[/tex]
[tex]\\ \\ =296f{ t }^{ 2 }+168f{ t }^{ 2 }+96f{ t }^{ 2 }+72f{ t }^{ 2 }\\ \\ =632f{ t }^{ 2 }[/tex]
Therefore the answer is: C
The side that is facing you has a surface area:
[tex]64f{ t }^{ 2 }+84f{ t }^{ 2 }=148f{ t }^{ 2 }[/tex]
The side exactly opposite this one has the same surface area - 2 sides with this surface area in total.
The bottom side has a surface area:
[tex]84f{ t }^{ 2 }[/tex]
The side to your right has a surface area:
[tex]84f{ t }^{ 2 }[/tex]
The side to your left has a surface area:
[tex]48f{ t }^{ 2 }[/tex]
The side to your top left has a surface area:
[tex]48f{ t }^{ 2 }[/tex]
The side beside the side to the top left has a surface area:
[tex]36f{ t }^{ 2 }[/tex]
The side at the very top has a surface area:
[tex]36f{ t }^{ 2 }[/tex]
Combined, the surface area is:
[tex]S=2\cdot 148f{ t }^{ 2 }+2\cdot 84f{ t }^{ 2 }+2\cdot 48f{ t }^{ 2 }+2\cdot 36f{ t }^{ 2 }[/tex]
[tex]\\ \\ =296f{ t }^{ 2 }+168f{ t }^{ 2 }+96f{ t }^{ 2 }+72f{ t }^{ 2 }\\ \\ =632f{ t }^{ 2 }[/tex]
Therefore the answer is: C
