if you understand surface area can you please help me with this problem? 9th grade geometry. thanks!?

[TRish]

https://twitter.com/PashaEquestrian/stat...48/photo/1

i dont get it, please help, surface area confuses me alot.

[Samwise]

This whole surface of this figure can be broken down into rectangles, and the areas of rectangles are very easy to calculate, so we can just add them all up.

There are two upside-down T-shaped faces (front and back of the stand), and they have the same area.
Let's treat each of them as two rectangles, one the "stem" of the T and the other the cross-bar. Each of these has a length of c and a width of x, so the total is
2 (2 (xc)) = 4xc = 4 (4 in) (20 in) = 4 (80 square in) = 320 square in.

The rest of the stand is a whole series of rectangles n wide.
Each of these has an area n times its length.
To save time, let's add up all the lengths and multiply the total by n (8 in).
That's easier because we just have to add up the perimeter of one of the T faces.

Starting with the bottom of the stand:
c + x + w + c + x + c + w + x
= 3c + 3x + 2w
= 60 in + 12 in + 16 in
= 88 in for the perimeter

88 in * 8 in = 704 square in

Adding that to the surface area of the T-shaped faces, we get a total of
704 + 320 = 1,024 square inches
which is answer D.