Kailee1423
  • Kailee1423
I need help with a few questions that I got wrong on my homework. 1.Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. (Pic in comments) 2.Find the volume of the square pyramid shown. Round to the nearest tenth if necessary. (Pic in comments)
Mathematics
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schrodinger
  • schrodinger
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Kailee1423
  • Kailee1423
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Kailee1423
  • Kailee1423
3.Find the volume of the square pyramid shown. Round to the nearest tenth if necessary. 4.Find the volume of the given prism. Round to the nearest tenth if necessary.
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Kailee1423
  • Kailee1423
@phi @mathway

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phi
  • phi
which one do you want to do?
Kailee1423
  • Kailee1423
We can start on the first one if you don't mind:) I just don't understand them.
phi
  • phi
Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. lateral area is the "side area" , which is the area not including the "top or bottom" That is not very clear, but we we assume the top and bottom are the triangles and that means the "sides" are the 3 rectangles.
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phi
  • phi
The first step to doing this is find the length and width of each side can you say what the length and width of the "bottom rectangle" is ?
Kailee1423
  • Kailee1423
23 and 9
phi
  • phi
and the area of a rectangle is length * width so the area of the bottom side is 23*9
Kailee1423
  • Kailee1423
Which sides do you do this to?
phi
  • phi
we are finding the area of the sides that are "rectangles" this is the bottom side of the prism |dw:1441657465989:dw|
Kailee1423
  • Kailee1423
And the top would be 23*12.04?
phi
  • phi
yes
Kailee1423
  • Kailee1423
Do we need to do the back too? If we did then I think it would be 8*23
phi
  • phi
yes. also the back. I am assuming the prism has "sides" and a "top and bottom" the top and bottom will be the two triangle faces (top and bottom should look alike) that leaves the 3 rectangles as the "sides" (even though the prism is laying on its side)
Kailee1423
  • Kailee1423
Ok. Is there a reason why the rectangles couldn't be the top and bottom?
phi
  • phi
It is "convention". (It is also sometimes not obvious) but in this case, with 3 sides, it is hard to argue 2 of them are the top and bottom (and the two triangle faces are sides). so just assume: we have more than two sides, and the sides all have the same shape. we have a top and bottom, and those two have the same shape.
Kailee1423
  • Kailee1423
Ok that makes sense
phi
  • phi
in this figure we have 3 rectangle faces and 2 triangle faces. so sides will be the rectangles and the 2 triangles will be the top and bottom.
phi
  • phi
so the lateral area will be 207+276.92 + 184= 667.92 rounded to the nearest whole number: 668
phi
  • phi
for the surface area (which is the lateral area plus the top and bottom) we need to add in the area of the two triangles can you figure the area of a triangle? height is 8, base is 9
Kailee1423
  • Kailee1423
8*9 is 72 and if the other side is the same then the two together would be 144. Is that the surface area?
phi
  • phi
the surface area is the total area. so add 72 to the lateral area to get the surface area
Kailee1423
  • Kailee1423
Would I need to add 72 or 144?
phi
  • phi
** if the other side is the same *** yes, it is. You use the idea that opposite sides of a rectangle are equal thus |dw:1441658469941:dw|
phi
  • phi
the area of a triangle is 1/2 base * height
phi
  • phi
so you have 1/2 * 8 * 9 = 36 and the other triangle is the same 8 by 9 size so another 36 total of *both* triangles is 72
Kailee1423
  • Kailee1423
Oh I left out the 1/2. I get it now
phi
  • phi
surface area is 667.92 + 72 (notice we should always use the most accurate number) after we add up, then round to get the final answer.
Kailee1423
  • Kailee1423
Would you like me to make a new question for the next one or do you want to just stay here?
phi
  • phi
please make a new post. they get too long otherwise.
Kailee1423
  • Kailee1423
Ok I'll tag you in it. Thank you so much!

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