Question

Ho do you get the Surface Area of this shape?

Answer 1

This solid object contains 8 sides.

The side that is facing you has a surface area:

$64f{ t }^{ 2 }+84f{ t }^{ 2 }=148f{ t }^{ 2 }$

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:

$84f{ t }^{ 2 }$

The side to your right has a surface area:

$84f{ t }^{ 2 }$

The side to your left has a surface area:

$48f{ t }^{ 2 }$

The side to your top left has a surface area:

$48f{ t }^{ 2 }$

The side beside the side to the top left has a surface area:

$36f{ t }^{ 2 }$

The side at the very top has a surface area:

$36f{ t }^{ 2 }$

Combined, the surface area is:

$S=2\cdot 148f{ t }^{ 2 }+2\cdot 84f{ t }^{ 2 }+2\cdot 48f{ t }^{ 2 }+2\cdot 36f{ t }^{ 2 }$

$\\ \\ =296f{ t }^{ 2 }+168f{ t }^{ 2 }+96f{ t }^{ 2 }+72f{ t }^{ 2 }\\ \\ =632f{ t }^{ 2 }$

Therefore the answer is: C