Surface area of a box (cuboid)

let's see if we can figure out the surface area of this cereal box and there's a couple of ways to tackle it the first way is well let's figure out the surface area of the sides that we can see and then think about what the surface area of the sides that we can't see are and how they might relate and then add them all together so let's do that so the front of the box is 20 centimeters tall and 10 centimeters wide it's a rectangle so to figure out its area we can just multiply 20 centimeters times 10 centimeters and that's going to give us 200 centimeters 200 centimeters or 200 square centimeters I should say 200 square centimeters that's the area of the front and let me write it over here as well 200 now we also know there's another side that has the exact same area as the front of the box and that's the back of the box and so let's write another 200 square centimeters for the back of the box now let's figure out the area of the top of the box the top of the box is we see it's 3 the box is 3 centimeters deep so this right over here is 3 centimeters 3 it's 3 centimeters deep and it's 10 centimeters wide we see that the box is 10 centimeters wide so the top of the box is going to be 3 centimeters times 10 centimeters which is 30 square centimeters of area so that's the top of the box 30 square centimeters well the bottom of the box is going to have the exact same area we just can't see it right now so that's going to be another 30 and we have 2 more sides because this box has 6 sides we have this side panel that is 20 centimeters tall we see that the height of the box is 20 centimeters and 3 centimeters deep so 3 times 3 times 20 3 times let me write that a little bit neater 3 times 20 that's 20 centimeters right there 3 centimeters times 20 centimeters is going to give us 60 square centimeters 60 square centimeters now that's this side panel but there's another side panel that has the exact same air that's on the other side of the box so 60 centimeters squared or squared centimeters for this side and then another 60 for the corresponding side opposite to it that we can't see and now we can just add up all of these together and so we get 0 let's see this is going to be carry the one or regroup the one it's a 100 and then we have 500 so we get 580 square centimeters is the surface area of this box