Question

Identify the surface area of the composite figure.

Answer 1

A. S = 524 in2
B. S = 477 in2
C. S = 513 in2
D. S = 533 in2

Answer 2

I'm not sure if it means the cube on top, or if it means the larger cube underneath it.

Answer 3

Slow down. There is no rush here.

Look at the cube atop the rectangular prism.

Answer 4

Sorry. I have that issue of getting impatient. I'll try not to be.

Answer 5

The cube has 6 faces but one of them is not exposed because that face is resting on the lower figure.

What is the area of a square with length and width 3" ?

Answer 6

It's okay to be impatient but in mathematics, I have found it causes me to mess up.

Answer 7

What is the area of a square with length and width 3" ?

Answer 8

Would it be 9" ? And alright.

Answer 9

Yes. How many of those squares of area 9" are exposed.

Answer 10

3?

Answer 11

4?

Answer 12

Look again.

A cube has 6 faces. Those faces are squares.

Answer 13

On top you don't really see the back or underneath it.

Answer 14

That is because we are looking at a 3-D diagram in 2-D.

Put a number die on top of a shoebox and you will see the exposed faces of the cube. All 5 of them.

Answer 15

Yeah. You for sure don't see the one underneath though. It's resting on top.

Answer 16

Underneath doesn't count. We are doing the surface area of the composite figure.

If we were to paint the composite figure, we would not paint the base of that cube.

It is stuck to the rectangular solid.

Answer 17

Right..

Answer 18

Five faces at 9 square inches each is how much
"exposed" area for the cube.

Answer 19

What is 5*9 =

Answer 20

45.

Answer 21

Now, for the lower solid.

There are 6 faces.

Two are 14 by 6 rectangles.

Two are 8 by 6 rectangles.

Two are 14 by 8 rectangles.

Answer 22

Do you recall how to get the area of a rectangle?

Answer 23

Width by the length for area.

Answer 24

Yes.

Crank this out:
2*14*6 + 2*8*6 + 2 * 14 * 8 = ?

Verify that those are the correct dimensions of the 6 faces.

Answer 25

168...+16*6=96 um..equals 264 + 28 = 292.. wait holdon

Answer 26

28*8=224 so 264+224 = 488

Answer 27

Yes. By the way, you can copy and paste that string of numbers in the Google search box and get an answer. The Google calculator pops up with the answer.

Answer 28

One of the choices isn't 488 though. Only 477.

Answer 29

Where the cube is sitting on top of the rectangular solid is surface area of the rectangular solid that has been included in the 488.

So, the extra 9 square inches must be subtracted from 488 to get 479.

Answer 30

I assume that the composite figure's base is "exposed" and is supposed to be included in the surface area calculation. From the problem, there is no way to know.

Answer 31

479 + 45 = ?

Answer 32

@Calamitylikespie

Answer 33

524.

Answer 34

Is that an option?

Answer 35

Yes. Thank you!!