Question

Geometry questions.

Answer 1

@whpalmer4, can you help?

Answer 2

Euler's formula is very cool, but I always need to figure out what it is each time :-) Hang on a sec...

a cube has 12 edges and 8 vertices and 6 faces

V + F - E = 2

Answer 3

17+25-40=2?

Answer 4

So 40 edges?

Answer 5

And the second is 10 vertices.

Answer 6

Do you have time for a couple more questions?

Answer 7

40 edges, 10 vertices, that's correct

Answer 8

whatchagot?

Answer 9

Here are two more.

Answer 10

how many sides on the cross-section?

Answer 11

I don't know what is the cross section.

Answer 12

the shaded area in the drawing is the cross-section

Answer 13

5, so pentagon.

Answer 14

very good

Answer 15

How do I find the lateral area?

Answer 16

find the area of each of the faces and add them up

Answer 17

don't include the base, however...

Answer 18

I got 322

Answer 19

yeah, that includes the base, right? every definition I've seen of lateral area says don't include the base, but if you don't include the base, none of the answers are possible...

Answer 20

I would interpret this as meaning the problem author really meant surface area, not lateral area. And in that case, 332 is the correct answer, not 322

Answer 21

I got 322 with the area of all the rectangles. I excluded the triangle bases.

Answer 22

2 triangles with base 5 and height 2 = 2*(1/2)*2*5 = 10
base = 26*5 = 130
slanting face = 5.39*26 = 140
back side = 2*26 = 52
total = 332

but the two triangles aren't bases

Answer 23

do you see any indication that they are?

Answer 24

Well, I thought that in a triangular prism, the two triangles were the bases.

Answer 25

I suppose if you interpret the prism as standing on end (which it isn't shown doing in the diagram), then you would not include the triangles and the lateral area would be just the area of the various rectangles

Answer 26

Yeah, I see what you mean.

Answer 27

Hmm, well, I guess your interpretation allows for choosing an answer without assuming an error on the part of the problem author, so that's probably what they want.

Answer 28

Ok, thanks for all the help. I'm still going with 322 then.

Answer 29

I do see some people I trust referring to the triangular ends as the base of a triangular prism, but this is the first time I've heard of it. Maybe I wasn't paying attention before :-)

Answer 30

Yeah, I think I would go with 322 in light of this discussion

Answer 31

ok, :)

Answer 32

though to me, the base of the prism is the thing it is resting on!

Answer 33

what next, the Eiffel tower is actually standing on one of its sides? :-)

Answer 34

Well, the Eiffel Tower is more of a pyramid shape, meaning that the base would be the square.