Observe the composite figure below.
The bottom shape is a cube with base edges of 16 meters. The top shape is a right pyramid with a height of 15 meters. What is the surface area of this composite figure?
Answer
544 m2
1,280 m2
1,824 m2
2,080 m2

- anonymous

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- anonymous

##### 1 Attachment

- darthsid

What's your working so far? How are you approaching this?

- anonymous

i have made it absolutely no where on this problem.

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## More answers

- darthsid

Do you know what the area of a square is?

- anonymous

yesss

- darthsid

Great! So try to divide the figure into two parts:
1. the pyramid
2. The cube

- darthsid

Now, a cube's surface is basically 6 squares, so what would the area of the surface of the cube be?

- anonymous

256???

- darthsid

That's the area of one square. A cube's surface is made of 6 squares. So the surface area of the cube is 6 times the area of a square, right?

- anonymous

so that would be 1,536

- darthsid

Yeah, so that's the surface area of the bottom part.
Now let us look at the top part, it is a right pyramid, which is basically 4 triangles and a square on the surface

- darthsid

DO you have the formula for the surface area of a right pyramid?

- anonymous

B+ 1/2ps?

- anonymous

yes

- darthsid

Exactly, for the pyramid your main problem is finding s
what's the formula for s?
You're very close!

- anonymous

i have no idea ! haha

- darthsid

B is the area of the base, which is a square, which you calculated above was 256! P is the perimeter of the base, which is the sum of all sides of the base,
So P = 16 + 16 + 16 + 16 = 64

- darthsid

So we are left with s, which is the slant height. Slant height
\[s=\sqrt{{h^2}+{r^2}}\]
where h is the height, and r is the radius of the base
The radius of the base is half the side of the square, so r = 8.
Can you calculate s?

- anonymous

289?

- anonymous

17

- anonymous

nno 288

- anonymous

16

- darthsid

No no, square root that! You are on the right track tahtah99 :)

- darthsid

yess, 17!

- darthsid

So, you said the formula was
B + 1/2Ps
B = 256 (area of square)
P = 64 (perimeter of square)
s = 17
So total surface area of the pyramid is?

- anonymous

800 ?

- darthsid

Great! That's correct.

- anonymous

see i told you!!

- anonymous

you got it!!

- anonymous

-_____- hahah

- darthsid

So now, you have a pyramid and a cube
Area of pyramid = 800
Area of cube = 1536
Now if you join the two, you will not see one side of the cube, and the base of the pyramid. Do you understand that?

- darthsid

It's not done yet :D

- anonymous

dont celebrate, its not done yet!!

- anonymous

oh Lord..
yeah i understand

- darthsid

So you have to subtract the area of two things:
1. The base of the pyramid
2. One square from the cube.

- anonymous

so subtract 512?

- darthsid

So your final area will be:
1536 + 800 - (area of 1 square) - (area of 1 square)
= 1536 + 800 - 256 - 256

- darthsid

Exactly! You got this!

- anonymous

exactly!! WHAT I SAY?? YOU GOT IT!

- anonymous

is the answer c?

- anonymous

THATS WHAT IVE BEEN TRYING TO SAY!! YES IT IS!!!!!!

- darthsid

Yes it is!

- darthsid

Congrats :)

- anonymous

thank you so much ! : )

- anonymous

SEE! NOOOOOWWW YOU CELEBRATE!!

- anonymous

YOUR VERY WELCOME~!

- anonymous

hahahahahahha

- darthsid

Glad to help!

- anonymous

glad to help too!

- anonymous

could you check my answer for the last question ?

- anonymous

nvm got it

- anonymous

ok.

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