[IMPORTANT] I don't know how to solve this problem

[Hyydrxzen]

Hi to everyone,
do you know the "One World Trade Center"?

Well, i've to calculate two things about it:

-The volume, according to its particular shape
-The surface of the glass plates which cover the whole structure

Searching on internet i found two dimensions:
1) Total height without antenna: 417 m
2) Cubic base dimensions: 61 m, for every side

Thanks for your attention, I hope you will see this message!

 

[Deleted member 4993]

Hi to everyone,
do you know the "One World Trade Center"?

Well, i've to calculate two things about it:

-The volume, according to its particular shape
-The surface of the glass plates which cover the whole structure

Searching on internet i found two dimensions:
1) Total height without antenna: 417 m
2) Cubic base dimensions: 61 m, for every side

Thanks for your attention, I hope you will see this message!

Assume that you have a square prism with foot-print 61 m X 61 m and height 417 m.

What is the volume of that prism?

What are the surface areas of the rectangular sides?

Please share one of your attempts with us.

Please share your thoughts about this assignment.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

 

[Hyydrxzen]

I don't know how to start, the faces are triangular and I can only calculate the straight ones. I don't know how to find the turned triangles dimensions.

 

[Deleted member 4993]

I don't know how to start, the faces are triangular and I can only calculate the straight ones. I don't know how to find the turned triangles dimensions.

Assume that the building faces are not triangular - those can be assumed to be rectangular (later we will correct it).

With that assumption,

what answers do you get?​

 

[Dr.Peterson]

Hi to everyone,
do you know the "One World Trade Center"?

Well, i've to calculate two things about it:

-The volume, according to its particular shape
-The surface of the glass plates which cover the whole structure

Searching on internet i found two dimensions:
1) Total height without antenna: 417 m
2) Cubic base dimensions: 61 m, for every side

Thanks for your attention, I hope you will see this message!

I don't know how to start, the faces are triangular and I can only calculate the straight ones. I don't know how to find the turned triangles dimensions.

I suppose you are talking about the current One World Trade Center, not the original.

This is not a prism, but an antiprism:

One World Trade Center - Wikipedia

en.wikipedia.org

From the 20th floor upwards, the square edges of the tower's cubic base are chamfered back, shaping the building into eight tall isosceles triangles, or an elongated square antiprism. Near its middle, the tower forms a perfect octagon, and then culminates in a glass parapet, whose shape is a square oriented 45 degrees from the base.​

Have you found more detailed dimensions?

I suggest starting with the surface area. You will need to know the height of each triangle, and its base (different for those pointing up and those pointing down), and then it will be easy.

For the volume, I can show you some formulas when you are ready, if I haven't already given you a good enough clue for finding them.

 

[Hyydrxzen]

No, I searched for an half hour but I haven't found any detailed dimension excluding the height and the base. I'm totally confused, especially because I don't know how to find the areas of the pointing-down triangles.

 

[Dr.Peterson]

No, I searched for an half hour but I haven't found any detailed dimension excluding the height and the base. I'm totally confused, especially because I don't know how to find the areas of the pointing-down triangles.

As far as I can tell, the base is a square 61 m by 61 m, as you said, and the sides go straight up 20 stories, so you can estimate how high that would be, and work it as a square prism.

The dimension I'm not sure of is the sides of the turned square at the top; but some descriptions suggest that the corners would be directly above the midpoints of the sides of the base, so that the top would have exactly half the area of the base.

The altitudes of the triangles pointing down will be not quite vertical, but close enough that you can take all the triangles as having the same altitude (namely, the height of the building minus the first 20 stories).

When you get to volume, you might look up "antiprism" or "prismatoid", which is a broader class of solid including antiprisms. You'll probably have to do a little work to adapt the formulas you'll find.