Question

MEDAL + FAN Please help

What is the surface area of the composite figure?

Photo is attached

256 cm^2

384 cm^2

512 cm ^2

544 cm^2

Answer 1

Can you re-write the choices in numbers?

Answer 2

ok

Answer 3

Done

Answer 4

And I will show you how to do it.

You have 2 rectangles
BOTTOM: 4 on 4 on 8
TOP: 4 on 4 on 24

Answer 5

or one rectangle 2 cubes :/

Answer 6

You have 2 'cubic' rectangles. I mean 3D rectangles.

Answer 7

yes 1 rectangular prism 2 cubes

Answer 8

Ohh, wait you are looking for surface Area, so I am incorrect.

Answer 9

you also must subtract interior faces, I did everything and got something like 575

Answer 10

Wait, I can only count the faces that I can see, but not all of them ?

Answer 11

OHHHHHHHHHHH wait I see what I did wrong

Answer 12

you see you split up the figure into smaller figures, when you do that, extra faces become visible that aren't going to be covered in the actual equation, so you have to kind of subtract those from the actual area

Answer 13

there are 4 interior faces I missed thats why my answer came out wrong

Answer 14

yes, but first, I am trying to find all faces of two rectangles as if they are separate, and then subtract the faces they have in common.

Answer 15

And you are right, the only face that is not actually there is the 4 by 4 face.

Answer 16

yeah but when the 4 by 4 faces connect there are actually 2 4 by 4 areas you have to subtract, and the 4 by 4 face on the top

Answer 17

So the answer is actually 544

Answer 18

so when you add the surface area for all of the 3d figures up you get 608, but 608 - 16 - 16 - 16 - 16 = 544 :)

Answer 19

BOTTOM rectangle: 4 on 4 on 8
TOP rectangle: 4 on 4 on 24
then the face 4 by 4 is 16.

bottom rectangle: 2(4×4)+2(4×4)+2(4×8)
top rectangle: 2(4×4)+2(4×4)+2(4×24)    ────────────
4(4×4) + 4(4×4) + 2(4×8) + 2(4×24)

4(4×4) + 4(4×4) + 2(4×8) + 2(4×8×3)

4(4×4) + 4(4×4) + 2(4×8) + 6(4×8)

4(4×4) + 4(4×4) + 8(4×8)

4(4×4) + 4(4×4) + 8(4×4× 2)

4(4×4) + 4(4×4) + 16(4×4)

(4+4+16)(4×4)

(24)(4×4)

Answer 20

There are 24 '4 by 4' faces.

Answer 21

Subtract 1 4 by 4 face that is not actually there.
you get `23(4 × 4)` and the exact answer is 368.

Answer 22

Well technically thats not in my answer choices