Question

What is the surface area of the composite figure?
attachment below

Answer 1

Try calculating the surface area of the largest face first. That may make it easier.

Answer 2

i did that and got 416 and i did the bottom and got 160. added them together and got 576 but that isnt on my answer choices

Answer 3

did you put into consideration that there are sides of the figure that aren't readily visible? Did you calculate the area of those too?

Answer 4

yes i did. i am still confused.

Answer 5

Lemme try to work it out here quickly.
1. The largest face in direct view
A = (8*4)+(24*4) = 128
2. The largest face not in view. A = 128
3. Faces viewed from above the figure.
A = (28*4) = 112
4. Faces viewed from below the figure. A = 112
5. Faces viewed from the right side of the figure.
A = (8*4) = 32
6. Faces viewed from the left side of the figure. A=32
TOTAL SURFACE AREA = 128+128+112+112+32+32 = 544

Answer 6

I hope you notice that you can re-shape the figure into a cuboid by shifting the positions of some of the faces. That will have no effect on the surface area, and will make calculations much easier. Notice the repetition of 128, 112 and 32 to represent the areas of the faces of the cuboid I sketched.

I hope that helps.