Hello, so I am currently not doing so well in Geometry as i have a D. I have never been very good at asking teachers for help. Think any of you guys can help me? Thank you!

My usual policy of not giving complete answers where I can is in effect. A curious choice of labels for that first one -- were it an engineering drawing it would probably be called over constrained, however if they don't want you to have to calculate another I guess it plays. Anyway there are a variety of approaches but imagining it as a cuboid is probably not of much use here, at least not in full -- no sense making life hard if you have two identical right angle triangles you can imagine as a square and just do 6x9. Other than that it is just plain areas of a square and adding it all up, ignoring the base when it asks you about the lateral area. Bonus is the differences between the two values in the multiple choice there are different so in a hurry or as a check you could see the base area, figure out the differences and then check it. Sometimes the test maker might have messed up and left only one right answer. You have to figure out the area of each face and add them together, or in the case of lateral area then leave out the base area (seems a pointless thing to teach but that is not why we are here). 2) pi x radius squared is the area of a circle. pi x diameter is the circumference, which also happens to be the edge of the quadrilateral you get if you unwrap it. The length/height of the cylinder is the other measurement for that quadrilateral. Bonus is they are the same so it is actually 12X12Xpi + the circle end caps Choice video 3) There are a couple of ways to look at this. The way I would use though as you have a simplified problem in this case lsa = pi x radius x slant height You know lsa and you know radius, pi is a number so you now need to solve for slant height. Do note that you have 500xpi as the area, the typography on your work sheet is bad though so be careful. It does also mean pi cancels out of the equation when you are rearranging it.

Try to imagine each surface as a flat shape and just add them up. I'm about to finish Calculus 3 next Wednesday and we literally just integrate everything... Like, if you think about it, a cylinder is actually just two circles and a rolled up rectangle. A cube is actually 6 squares. This works with all easy shapes. I'd also like to add that I've never used lateral area.

Neither have I. From what I can tell from the problems here it's just whatever the rectangles added would be

Yeah, with lateral area you ignore the area of the bases, actually making it easier because you just have to multiply the perimeter of the base by how long the prism is. So, like for #5 the perimeter of the triangle would be 6m + 9m + sqrt(117). This adds up to 25.81665m. The prism is 26m long so 25.81665m*26m= 671.233...m^2 = lateral area (looks like they only want 3 sig figs so it's 671m^2) Since we already got the lateral area we can just add the area that makes up the 2 triangles to the lateral area. The area of a triangle is (base*height)/2 ,but since we have 2 triangles we can ignore the 1/2. So 6m*9m=54m^2. And 54m^2 + 671m^2= 725m^2 and that's our surface area.

The volume of a cylinder is the area of the circumference * it's height. So pi*(6inch^2)*12inch = 36inch*12inch*pi = 432*pi inch^2 Sorry if the inches abreviation is wrong, I'm used to SI units, like metres Besides that, I'm not sure what it's referring to when it says "lateral area" and "surface area". Aren't they the same thing?

i think he doesn't need the volume just the surface and lateral area. Even in the US we mostly use SI units. @BurningDesire If you read my explanation in the previous post you should be able to get 6. #12 might by a little trickier though. Imagine a cone made of a rolled up paper. If you were to unroll it it would be the sector of a circle. Let me see if I can put up a picture. I made a mistake in the original picture! I forgot to multiply by pi when getting the circumference of the cone so the answer was actually just 10cm. Here I fixed it.

Hey guys, BurningDesire says thanks for the help, and because of you guys, he's is back up to a C in geometry. He just wanted me to inform you guys of that since he is suspended.