Surface area using a net: triangular prism (video) | Khan Academy

Video transcript

– What I want to do in this television is get some exercise 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 correct where I ‘m drawing this red, and besides right over here and right over there, and right over there and besides in the back where you ca n’t see merely 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 that improving, 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, veracious over here ? well in the web, that corresponds to this area, it ‘s a triangle, it has a basis of 12 and stature of eight. so this area right field over here is going to be one one-half times the foundation, thus fourth dimension 12, times the stature, times eight. indeed this is the lapp thing as six times eight, which is equal to 48 whatever units, or feather units. This is going to be units of area. So that ‘s going to be 48 feather units, and up hera is the accurate same thing. That ‘s the accurate same thing. You ca n’t see it in this figure, but if it was diaphanous, if it was transparent, it would be this rear right over here, but that ‘s besides going to be 48. 48 straight units. nowadays we can think about the areas of I guess you can consider them to be the side panels. So that ‘s a side panel correct over there. It ‘s 14 high and 10 wide, this is the other side panel. It ‘s besides this length over here is the same as this length. It ‘s besides 14 high and 10 broad. So this side gore 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 hearty units. This one is besides 140 squarely units. And then last we just have to figure out the sphere of I guess you can say the basis of the figure, so this hale region right over hera, 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 entire area is going to be, let ‘s see. If you add this one and that one, you get 96. 96 squarely units. The two magenta, I guess you can say, slope panels, 140 plus 140, that ‘s 280. 280. And then you have this base that comes in at 168. We want it to be that lapp coloring material. 168. One, 68. Add them all together, and we get the airfoil area for the integral calculate. And it was super valuable to open it up into this net income because we can make certain we got all the sides. We did n’t have to kinda rotate it in our brains. Although you could do that american samoa well. so, with six plus zero plus eight is 14. Regroup the one ten-spot to the tens set, there ‘s immediately one ten. sol one plus nine is ten, plus eight is 18, plus six is 24, and then you have two plus two plus one is five. So the surface area of this number is 544. 544 squarely units.

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