Surface Area and Volume of a Rectangular Prism Grade 7 Nelson Chapter 11 02 18 12

okay we're doing surface area and volume of rectangular prism okay so we got rectangular prism over here and what we're going to figure out is let's say we have these measurements on this rectangular prism it looks like it's about we're going to say it's 4 cm in height maybe 3 cm at the base and the depth we'll say is actually five okay say it's little harder so five CM so what we're going to have to do first of all to figure out surface area it's very similar to area Okay surf surface area we're going to just call SA is actually equal to the area of each face okay added all together so how many faces are on this object right now four well we have one yeah that's right and then here on the right two the one at the back three four and then bottom five six okay that's right so there's actually six faces to this so the surface area is going to be equal to what we're going to do is we're going to highlight certain areas okay so what we'll say is the front and back here's this guy one Ty the surface area right so those are the front and back we'll focus on those two to start and then we'll go through other ones okay so very first thing our the front and back two are going to have different or the same areas the same yeah they'll be the same so we really only need to figure out the area of one of them okay so let's think of it as just rectangle in itself what are the dimensions of that rectangle put it up here that's right the dimensions of this guy are 4 cm and 3 cm three so we're gonna find the area of that and how would find the area of that okay so area of the yellow one so area is equal to length time width right put them in Brackets and what's the length and the width sure did it matter which we called the length and the width not really so what's the area of this shape going to be 12 CM squ that's right 12 CM squar now there's two of them so what's the area of both of them together going to be yeah we just need to add them together that's right so we know the other one's going to be the same so what we're going to do is we're going to multiply that by two what we'll do is we're going to call this area A1 okay we'll say he's the area of the very first one we'll call him A1 put it up in the corner here so surface area is A1 Plus and the guy at the back we'll call A2 now they're going to be the exact same right so we have two of them and we'll move this down so we can continue with this formula so we have A1 and A2 those are the front and the back okay next what we're going to do is we're going to focus on the sides so I'll do those on in green so the side is going to be here here here here and the other side okay so we'll doal with those two sides now we got to figure out what the dimensions of those two sides are so I'm going to draw another little rectangle on the side here what are the dimensions of those sides yeah that's right so move this one down those ones are 4 cm and 5 cm so how do we find the area of one of the sides that's right length times width so we do the same thing again we're going to call this guy we'll label him this guy will be A3 okay the other other guy will be A4 are they going to be the same or different same so we'll just find the area of A3 area of A3 that is our length times our width okay so what is our length of that one going to be and the width okay so what's the area of it going to be good do we have to do the other side no we know it's going to be what yeah Al together it'll be 40 that's right so let's put our little formula down here again so we know the surface area is A1 Plus A2 + A3 plus A4 what we'll do here is I'm just going to write down A2 is equal to 12 cm squared because we know that right and we know that what good okay how many more faces do we got to deal with the botom the top and botom top and the bottom okay let me see if can get different color pen here we'll try with this guy actually there we go so now we're going to do with the top and the Bottom now same as before excuse me are these going to be different or same same they're going to be the same what are the dimensions of these two going to be all right so let's put little rectangle down here you know we're going to have one that's say something like that so it's not the scale because we can fit it in we'll say this is 5 cm and this is 3 cm okay what do you want to call the bottom one yeah that's great idea A5 and the top should be what A6 A6 good so let's solve A5 what's the area going to be uhhuh okay what's the length of it the width good so what's the area what's the area of A6 good now how many faces do we say this had six faces and we've solved the area of how many different shapes six different shapes so what's the last step we're going to need to do here that's right okay so what was the area of my A1 okay and A2 what about A3 A4 a56 okay good so have those all now let's quickly double them because we know they're going to be the exact same what's 12 and 12 24 what about 20 and 20 15 and 15 good now let's add these up good 94 what excellent so the surface area of this guy is 94 cm squared we had to find the area of all six faces right we did the started with the front and the back and we did the sides and then the top and the bottom okay we found the area of each one and we added them all together and that's how you find surface area of rectangular prism all right dealing with rectangular prism we'll give it the exact same measurements this was three and this was four right yeah so we have the exact same measurements now but this time we're going to deal with the volume of the shape now do you know what the volume of something is exactly length times the width time the height so in other words we only need three measurements to solve this when multiplying all three together okay what is my length going to be okay say that's our length what's our width going to be sure and what is our height going to be good we only need three dimensions here okay we're dealing with this think of it like what we're actually doing here is we're finding the area of maybe the bottom face 3 * 5 okay and then we're just multiplying it by the height it's like we have tons of them okay so it's like have one two three four slabs of it and that's why we multiply it by four we're finding that area of that one object and then we're compounding four more times there okay so when we go to plug it into this formula our volume equals what did we say the length was yeah then the width and the height do you know what this is going to be yes that's right to the power of three it's cubed there because we're dealing with one two dimensions and third dimension okay area we just deal with flat objects right so let's compare the two we're already done volume that's easy volume is in comparison right when we're doing area of an object see how it's flat we're just dealing with the flat part here volume means three dimensions so we put three area is two just length and width that's why we put the number two okay does that make sense so that's everything we've done there