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 has 2 centimeters. And any other edge that has

the same number of hash marks, in this case one, 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. 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 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 this

side– we’ll do this in orange, actually– when we

fold up that side, that could be this side

right over here, along this 2 centimeter edge. So that’s that side

right over here. When you fold this side in 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, of course, go on top of our

rectangular prism. So that’s the figure

that we’re talking about. It’s 5 centimeters

in this dimension. It is 2 centimeters tall,

and it is 2 centimeters wide. But let’s go back to

the original question. Is this thing’s surface

area 40 square centimeters? Well, the good

thing about this net here is it’s laid out all

of the surfaces for us, so 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

5 centimeters times 2 centimeters. So it’s going to be

10 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 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.