Ch 10 Lesson 3 Surface Area of Rectangular Prisms Video Lecture

so today's lesson is chapter 10 lesson three and it's surface area of rectangular prisms okay for the first problem problem one it says Roberta is wrapping gift for her sister's Kera she places it in box with the measurements shown number one says what is the area of one face of the box so you guys know face is just face is just side one side of the box so this is face this is face the sides are face the bottom is face is everybody with me okay so here we want to find the area of one face so if wanted to find the area of the front this would be 10 by 10 10 so 10 * 10 is equal to 100 so this is going to be 100 square in number two says how many faces the does the Box have so you even though you can't see them you know it has front and back that's two it has top and bottom that's two more and it has side and side so that's two more so they have how many sides six six very good so there's six sides there now it's number three says what operations would you use to find the surface area of the box so in other words what is if if we want to find out how much wrapping paper goes on the front and on the around the whole box what would do what operations would use addition subtraction multiplication or division multiplication we would multiply because we'd find the area of face and then what else and then we can add them all together right so we could use multiplication and addition the surface area of rectangular prism this is what we're talking about today the surface area or sa of rectangular prism prism with length and width and height is the sum of the areas of the faces in other words sum of course means that we're going to add very good we're going to add them and then to find the areas what are we going to do to find the areas we're going to multiply is every very clear so here if have if I'm looking at this box here okay we want to write make sure we write down this formula okay we've got we've got the front and the back and remember there's two of them exactly the same right the front and the back so so here we have 2 * the length time the height this is the length and the height right does everybody see that so this is the front and the back see it's the front and the back you see those are two congruent parallel sides right so that's the front and the back so that's length time height that's the front and the back okay then we also have this next part two * length time width so here's length here's length and here's width that's the top and the bottom so it's the top and the bottom do everybody with me on that and since there's two of them just need to find the area of one and multiply it times 2 that's why we have 2 * the length times width make sense all right and then we have the two sides so we have this side and to find the area of that side it's width times height so there's one here and there's one there is everybody with me okay and once again one two of them exactly the same that is the reason why we're multiplying times 2 here this is why we have the Formula 2 * the length * the height plus 2 * the length * the width plus 2 * the height times the width there's front and back there's top in the bottom and then there's both of the sides please make sure you write down even this this red green and blue stuff that wrote here okay now down here is what each of these is what this box looks like if it's opened up okay for the surface area of the prism the sum of it it's the surface area is the sum of the areas of its faces so once again this box this is what it looks like when it's opened up Okay so we've got the top and the bottom there's the bottom and there's top we've got the two sides right here and here and then we've got the front and the back those two okay all right so for example it says find the surface area of the rectangular prism so here we want to find the area of the front and the back okay so that's the area is 48 for the front and the back so we're going to multiply 2 * the 48 for the sides it's 42 so we're we're going to multiply 2 * the 42 you with me and then for the top and the bottom it's 56 so we're going to multiply 56 * 2 so then we just add them all together we end up with 292 Square met is everybody clear all right so here let's do the got it so the first thing we want to do is we want to find the area of the front and the back so here are the front and the back okay so to find that area for the front and the back we're going to do two * the length times height so that's going to be 2 * 10 * 15 does everybody see where we're getting those numbers okay so the surface area is equal to 2 * 10 * 15 then we want to find the top and the bottom so the top and the bottom are these two do everybody see that now to find the area of this top and bottom okay there's the 15 but what am going to multiply 15 times times times 10 you see that yes you were so here there's the 10 that 10 is the same as this right here you got that so this is going to be let's do it in green this is also going to be 10 in so it's going to be 15 * 10 you got it so we're going to add that two cuz there's two of them 2 * 15 * 10 and now we want to get the sides so here are the sides now if want to get those sides what am going to multiply 10 * just 10 * 10 right so that's 10 * 10 and there's two of them so we're going to multiply times two so this is this is your formula this is your substitution and now we simplify to get the answer so 2 * 10 * 300 2 * 15 * 10 300 and then 2 * 10 * 10 is 200 and now you just add them together 8 so we have 800 in squared is everybody clear now remember this is surface area right so because it's surface area it's square units all right so now we're going to find surface area using that formula so now that we've derived the formula now all you have to do is is use it yeah so you can use Nets or models to find the surface area of rectangular prism you can also use surface area formula to find the surface area Okay so for example two it says find the surface area of this rectangular prism so first we're going to find the the area of the front and the back okay so the area of the front and the back there's the front and there's the back okay we are going to multiply since there's front and back two times the length which is seven times the height which is four when we multiply 2 * 7 * 4 we get 56 so now we want to do the top and the bottom so here's the bottom there's the top there are the shapes so to find the top and the bottom there's two of them so that's two time 7 * 5 which is is 70 you got that so here's the side there's one and there's the other one right so here what we're going to do the two because there's there's two sides right then we're going to multiply the height and the width so here this is the height you see it that's four now want this measure right here or that measure right there so that's going to be what five okay and that's where we're going to get that five so we have 2 * 4 * 5 which is 40 okay so now we have the front and the back we have the front and the back we have the top and the bottom and now we have the two sides and now to get the total surface area you just add them all together and we get 166 Square ft so now here's our got it problem this is the one we're writing down so we want to find the surface area of the rectangular prism so here's the formula there's our formula and we want the front and the back so to get the front and the back what are we going to multiply four * 2 so we're going to multiply 4 * 2 to get the front and the back right and because there's front and back there's two faces we're going to multiply times two so that's 2 * 4 * 2 does everybody clear with that all right so now take that one away we are going to look at the top and the bottom there's the top and there's the bottom is everybody good with those okay so to get the top and the bottom we're going to multiply what times what 4 * 3 very good so and then there's two sides our faces so we're going to multiply times two so 2 * 4 * 3 and now we're going to find the sides so here's one of the sides and there's the other side so what dimension do know here this is three and if go to the other side that's two so we're going to multiply two * 3 * 2 yeah so it's two because there's two sides right and then the area of the side is the 3 * 2 you with me so now we simplify to get our final answer so the surface area is equal to 2 * 4 is 8 * 2 is 16 then 2 * 4 is 8 * 3 is 24 and then 2 * 3 is 6 * 2 is 12 so now you just add all of those together and you get 52 squared is everybody clear and of course as just as reminder this is surface area so my units are units squared very good all right so geode is being sent as gift it is packed in box that measures 7 in Long 3 in wide and 16 in tall what is the surface area of the box so here these are the dimensions we've got 7 in long that's the length right then we've got 3 in wide that's the width very good and 16 in tall is the height it's 16 in tall so it's the height you with me all right so now to use our formula two * the length * the height plus 2 * the length time the width plus 2 * the height time the width there's my formula and all have to do now is substitute the numbers for the length the width and the height is it right clear so once we do that this is the second line is what we get right here then we simplify and then add them all together to get our total surface area which is 362 Square in