## tahtah99 Group Title 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 2 years ago 2 years ago

1. tahtah99 Group Title

2. darthsid Group Title

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

3. tahtah99 Group Title

i have made it absolutely no where on this problem.

4. darthsid Group Title

Do you know what the area of a square is?

5. tahtah99 Group Title

yesss

6. darthsid Group Title

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

7. darthsid Group Title

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

8. tahtah99 Group Title

256???

9. darthsid Group Title

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?

10. tahtah99 Group Title

so that would be 1,536

11. darthsid Group Title

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

12. darthsid Group Title

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

13. tahtah99 Group Title

B+ 1/2ps?

14. kk1022 Group Title

yes

15. darthsid Group Title

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

16. tahtah99 Group Title

i have no idea ! haha

17. darthsid Group Title

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

18. darthsid Group Title

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?

19. tahtah99 Group Title

289?

20. tahtah99 Group Title

17

21. kk1022 Group Title

nno 288

22. kk1022 Group Title

16

23. darthsid Group Title

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

24. darthsid Group Title

yess, 17!

25. darthsid Group Title

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?

26. tahtah99 Group Title

800 ?

27. darthsid Group Title

Great! That's correct.

28. kk1022 Group Title

see i told you!!

29. kk1022 Group Title

you got it!!

30. tahtah99 Group Title

-_____- hahah

31. darthsid Group Title

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?

32. darthsid Group Title

It's not done yet :D

33. kk1022 Group Title

dont celebrate, its not done yet!!

34. tahtah99 Group Title

oh Lord.. yeah i understand

35. darthsid Group Title

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

36. tahtah99 Group Title

so subtract 512?

37. darthsid Group Title

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

38. darthsid Group Title

Exactly! You got this!

39. kk1022 Group Title

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

40. tahtah99 Group Title

41. kk1022 Group Title

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

42. darthsid Group Title

Yes it is!

43. darthsid Group Title

Congrats :)

44. tahtah99 Group Title

thank you so much ! : )

45. kk1022 Group Title

SEE! NOOOOOWWW YOU CELEBRATE!!

46. kk1022 Group Title

47. tahtah99 Group Title

hahahahahahha

48. darthsid Group Title

49. kk1022 Group Title

50. tahtah99 Group Title

could you check my answer for the last question ?

51. tahtah99 Group Title

nvm got it

52. kk1022 Group Title

ok.