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)

- Kailee1423

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- Kailee1423

@phi @mathway

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- phi

which one do you want to do?

- Kailee1423

We can start on the first one if you don't mind:) I just don't understand them.

- 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

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

23 and 9

- phi

and the area of a rectangle is length * width
so the area of the bottom side is 23*9

- Kailee1423

Which sides do you do this to?

- phi

we are finding the area of the sides that are "rectangles"
this is the bottom side of the prism
|dw:1441657465989:dw|

- Kailee1423

And the top would be 23*12.04?

- phi

yes

- Kailee1423

Do we need to do the back too? If we did then I think it would be 8*23

- 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

Ok. Is there a reason why the rectangles couldn't be the top and bottom?

- 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

Ok that makes sense

- 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

so the lateral area will be 207+276.92 + 184= 667.92
rounded to the nearest whole number: 668

- 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

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

the surface area is the total area. so add 72 to the lateral area to get the surface area

- Kailee1423

Would I need to add 72 or 144?

- 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

the area of a triangle is 1/2 base * height

- 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

Oh I left out the 1/2. I get it now

- 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

Would you like me to make a new question for the next one or do you want to just stay here?

- phi

please make a new post. they get too long otherwise.

- Kailee1423

Ok I'll tag you in it. Thank you so much!

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