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# Surface area using a net: triangular prism

## Video transcript

what I want to do in this video is get some practice finding surface areas of figures by opening them up into what's called nets and one way to think about it is if you had a figure like this and if it was made out of cardboard and if you were to cut it if you were to cut it right where I'm drawing this red and also right over here and right over there and right over there and also in the back where you can't see it just now it would open up into something like this so if you were to open it up it would open up into something like this and when you open it up it's much easier to figure out the surface area so the surface area of this figure when we open it up we can just figure out the surface area of each of these regions so let's think about it so what's first of all the surface area what's the surface area of this right over here well in the net that corresponds to this area it's a triangle it has a base of 12 and a height of 8 so this area right over here is going to be 1/2 times the base so times 12 times the height times 8 so this is the same thing as 6 times 8 which is equal to 48 whatever units were 2 square units this is gonna be units of area so that's going to be 48 square units and up here is the exact same thing that's the exact same thing you can't see it in this figure if it was transparent if it was transparent it would be this backside right over here but that's also going to be 48 48 square units now we can think about the areas of I guess you can consider them to be the side panels so that's a side panel right over there it's 14 high and 10 wide this is the other side panel it's also this length right over here is the same as this length so it's also 14 high and 10 wide so this side panel is this one right over here and then you have one on the other side and so the area of each of these 14 times 10 they are 140 square units this one is also 140 square units and then finally we just have to figure out the area of I guess you could say the base of this figure so this whole region right over here which is this area which is that area right over there and that's going to be 12 by 14 so this area is 12 times 14 which is equal to let's see 12 times 12 is 144 plus another 24 so it's 168 so the total area is going to be let's see if you add this one and that one you get 96 96 square units the two magenta I guess you could say side panels 140 plus 140 that's 280 280 and then you have this base that comes in at 168 I want me to do that same color 168 168 add them all together and we get the surface area for the entire figure and it was it was super valuable to open it up into the snack because we can make sure we got all of the size we didn't have to kind of rotate it in our brains although you could do that as well so 6 plus 0 plus 8 is 14 regroup the the 110 to the tens place it's now 110 so 1 plus 9 is 10 plus 8 is 18 plus 6 is 24 and then you have ups and then you have 2 plus 2 plus 1 is 5 so the surface area of this figure is 544 544 square units