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# Surface area using a net: rectangular prism

CCSS.Math:

## Video transcript

Teddy knows that a figure has a surface area of 40 square centimeters the net below has 5 centimeter and 2 centimeter edges could the net below represent the figure so let's just make sure we understand what this here represents so it tells us that it has 5 centimeter edges so this is one of the 5 centimeter edges right over here and we know that it has several other 5 centimeter edges because any edge that has this double hash mark right over here is also going to be 5 centimeters so this edge is also 5 centimeters this is also 5 centimeters this is also 5 centimeters and then these two over here are also 5 centimeters so that's 5 centimeters and that's 5 centimeters and then we have several 2 centimeter edges so this one those 2 centimeters and any other edge that has the same number of hash marks in this case 1 is also going to be 2 centimeters so all of these other edges pretty much all the rest of the edges are going to be 2 centimeters now they don't ask us to do this in the problem but it's always fun to start with a net like this and try to visualize the polyhedron that it actually represents it looks pretty clear this is going to be a rectangular prism but let's actually draw it so if we were to we're going to fold this in we're going to fold this that way this will be you could view this as our base right over here we're going to fold this in we're going to fold that up and then this is going to be our top this is the top right over here this polyhedron is going to look something like this so you're going to have your base you're going to have your base that has a length of 5 centimeters so this is our base let me do that in a new color so this is our base right over here I'll do it in the same color so that's our base this dimension right over here I could put the double hash marks if I want 5 centimeters and that's of course the same as that dimension up there now when we fold up when we fold up this side this in orange actually when we fold up that side that could be this side right over here this side right over here along this 2 centimeter edge so that's that side right over here when you fold this right over here that could be that that's that side right over there and then when of course we fold this side in that's the same color let me do a different color when we fold this side in that's the side that's kind of facing us a little bit so that's that right over there that's that right over there color that in a little bit better and then we can fold this side in and that would be that side and then of course we have the top that's connected right over here so the top would go this would be the top and then the top would you of course go on top of our rectangular prism so that's the figure that we're talking about it's five centimeters in this dimension it is two centimeters two centimeters tall and it is two centimeters two centimeters wide but let's go back to the original question is this things surface area forty square centimeters well the good thing about this net here is it's laid out all of the surfaces for us and we just have to figure out the surface area of each of these sections and then add them together the surface area of each of these surfaces so what is the surface area of this one here well it's going to be five centimeters times two centimeters so it's going to be ten square centimeters same thing for this one it's going to be 5 by 2 5 by 2 this one is 5 by 2 so these are each 10 square centimeters and so is this one this is 5 long 5 centimeters long 2 centimeters wide so once again that's 10 square centimeters now these two sections right over here they're 2 centimeters by 2 centimeters so they're each going to be 4 square centimeters so what's the total surface area well 10 plus 10 plus 10 plus 10 is 40 plus 4 plus 4 gets us to 48 square centimeters or centimeters squared so could the net represent could the net below represent the figure that has a surface area of 40 square centimeters no this represents a figure that has a surface area of 48 square centimeters