Math Ch 10 Lesson 3 Surface Area of Rectangular Prism

hi boys and girls today we're gonna be learning about surface area of rectangular prism so similar to lesson one we're now jumping back to my tangler prism but instead of finding the volume of how much the rectangular prism holds we're going to find the area of 3d rectangular prism and so we want to know all the surface and area of all the faces that rectangular prism has which is 6 faces so sense can lessen predict two things that you'd be learning so you're to learn how to find the surface area of rectangular prism using specific formula you're also going to be knowing the relationship between the areas of each of the face of prism and its surface area as whole so this is just some vocabulary start up so to define surface we know that it's the outer face it's the outside or the exterior boundary of thing or an object and if you were to define area that's the number of square units needed to cover that's your keyword cover the surface of closed figure so you've been finding areas of 2d shapes in chapter 9 okay but today we're going to be finding the area of 3d object so now what's the surface area will surface area is the sum of all the areas right of all the faces of the 3d figure and an example would be this is really good example from real life the amount of wrapping paper you would need to cover box so box is rectangular prism so real world linked gifts Roberto is wrapping gift for her sister skinned Sanada she places it in box with the measurements shown so as you can see right here this is cube because this is square and all of these six faces are all the same size and shape so they are congruent figures so cubes have six faces we got the front we got the back we got the right side left side top side and bottom side okay so says what is the area of just one face of the box so if one face we're going to say the front of it the one that we can see that's in the grid so just that's gonna be one face so what we're gonna do is we know how to find the area of square which is the same thing as rectangle which is length times width so would use these two numbers here that I've highlighted ten times times so length times width okay so then therefore that gets me to hundred square inches and if you can see kind of disregarded this number because that has nothing to do with this first face here okay so then just made note here that it's length times width and we have two bottom alright to top and bottom faces so that's one that's two and we have our left and right so that's another two one and two and we got our front and back which is the one on the front here and then one all the way in the back so that makes up total of six faces so two plus two plus two gives me six faces so this cube has six faces so that answers questions to how many faces does the box have and then right here says what operation would you use to find the surface area of the box well since you found out that example one had hundred square inches that is one face and all you did was you multiplied ten times ten which is multiplication that you used right over here ten times ten that's just to find one face now you would need to find the amount to cover the entire box right at the amount of wrapping paper so then therefore you're gonna need to either add up all the areas by all the faces so if there's six faces total and if they're the same exact shape and size well know that it's gonna be hundred times six right so if were to figure out the whole surface area of this entire cube it would be 600 inches and if we're working with air surface area we have to remember to square it okay so for this lesson make sure you get your measurements correct by putting square at the end of your measurements so we're using both multiplication and addition so multiplication first to find one face and then you're gonna use addition to add up all of the other faces of all the other areas alright so surface area of rectangular prism the word surface area so from now on we're gonna call it that sounds our surface area of rectangular prism with the length notice how they write the like that so it doesn't look like number one right so it's kind of like the cursive you have your width and you have your height is the sum that's adding of the areas of the faces so this is gonna be your formula that you're gonna need to memorize and it's kind know it's little bit difficult to memorize but I'll show you way as to how to remember that so surface area equals two times length times height plus two times length times width plus two times height times width so there's lot of things going on here and kind of labeled this for you the color green that's gonna be the one that's the length times your height so then your height would be this one here which is the same exact height as this one here so we can just move this height over so it'll be length times height and we use times two because if you notice this is the front side of it and that back side which is right here that I'm gonna outline that's the same exact size and shape so you to use the same exact thing so length which is this length here is the same thing as this length here times this height and then we have plus because we need to add up our other faces so we have our the yellow portion which is the top and bottom so once again - meaning that there's top and there's bottom so the top is yellow and right here's the other bottom right here that I'm outlining okay so we have our length so this length I'm going to move it up here we got our length times our width right if those right here with so I'm just gonna move this with up here so length times width and since there's two need multiply to double it by multiplying by two and then I'm gonna add your left and right side so I'm gonna call these the sides right we have our height and our width so we got our height and our width so that's then blue and this is the left side so we have our right side that I'm gonna outline right here for you so this one will be our height and this is gonna be our width once again we're multiplying them together so every time you multiply that's just to find one face right of the prism so then you just need to remember to double them okay good if you want to know it's gonna be two plus two plus two that's total of six faces so what you're doing is you're finding the face of one blue the different face of the yellow different face of the green and then you're doubling each one of them because they have the identical congruent shapes right on the opposite side all right so then if you want to remember just remember to right and then to and then right here's to so if you notice two + 2 LW and then this one's the only part that's different right that doesn't have two this one you just get combined and together and then you're just going to multiply them here okay so this is gonna be your formula only to find rectangular prism so coming over here you're gonna notice that the surface area of prism is the sum of all of the areas of its faces so this is the entire prism that you've been seeing now this is an unfolding version of it this is called net boys and girls so nets are very helpful because it can allow us to see exactly what we're dealing with and what numbers we want to use so right here we have front and back so that's gonna be the green portion here we have our length times our height once again our length times our height and you have to double it so that's why it's + LH so that's 1 LH that's 2 LH so 2 LH now we got our top and bottom which is our yellow though the box that's colored yellow so we have our length times width since this is times our width right here so LW and then would double it by multiplying it - and then last thing over to sides which is in blue we have our height and width so height times our width once again our height times our width so make sure you carry your numbers over okay boys and girls if they pertain to it so then if you have to that will give you double it so you so HW + HW 2h now you're just gonna add up all of these together to get your formula so this formula is the same thing as this formula here it's just breakdown of it as to how you know this formula came to be so take look at our first example let's find the surface area of the rectangular prism so you have to first find the area of each pair that's your keyword pair of faces so you have total of three pairs so we got our front and back so I've labeled it for you that screen and the numbers that you're gonna be using I'm gonna be boxing them so our front and back once again to represents that there's gonna be two PI's are pair so pair has two of the faces so it's gonna be eight times six that's why boxed it here which gets me to to get 48 you know if it's 48 here this must be 48 as well so I'm just gonna double that and of course 48 plus 48 gives me 96 and then have our top and bottom that I'm working with that's gonna be in yellow so I'm gonna be working with 8 times 7 so know this 7 is right here but you can't this 7 is also the same exactly this 7 here so you can just carry that over so 8 times 7 will get me 56 now if this is 56 this must be 56 as well so I'm gonna double that by multiplying by 2 if add them up or multiply them by 2 should get 112 and then lastly have my sides right once again there's pair so things the faces are in blue have 6 times 7 which gives me 40 - that's my triangle numbers that I'm using so then if it's 42 here it's must be 42 right over here so I'm going to double that to get me 84 and now all I'm gonna do is I'm going to add up 96 plus 112 and plus 84 to get me 292 or you can just choose to add up all these numbers just like how they did right over here and then do not forget to put squared meters because you are dealing with area at the end of the day okay so make sure you square it alright taking look at this next part it says find surface area using using formula you can use nets or models to find the surface area of rectangular prism you can also use surface area formula surface area equals 2 times length times height plus 2 times length times width plus 2 times height times width all right so this is example 2 but find the surface area of the rectangular prism you're going to first find the area of each face so this is the net of the model right over here that's given so everything that I've highlighted in blue that's our front and back so front and back we're using these two numbers so this is that the front this one's the back so seven if you know this is seven seven same thing here times four now four is also right over here so 7 times 4 gives me 56 ok sorry 7 times 4 doesn't it gives me 28 but 28 plus 15 28 times 2 would give me 56 so then I'm doubling it and then now I'm working on my top and bottom so my top right here would be 5 right times 7 once again 5 times 7 gives me 35 double that should get me 70 and then last name working with my left and right sides have 5 times 4 gives me 20 well then double that 20 plus 20 gives me 40 and then just need to add up all these numbers so 56 plus seventy plus 40 will give me 166 square feet okay and then example 3 says find the surface area of the rectangular prism to find the area of each face determine the dimensions we got our length we got our width and our height so because they're given to you like this all you have to do is just plug them into the formula ok so have my front and have my back so that will be 7 times 6 so that'll be length and height so length this is my length and have my height which is 6 so then if double that so 42,000 gave me 42 double 42 who get me 84 and then have my top and bottom which is my length and my width so my length is 7 again and then my width is 4 point 8 centimeters so 7 times 4 point 8 double that should get me 67 point two now have my two sides which is 2hw that would get me my height is 6 and then my width is 4 point 8 so multiply that double it should get 57.6 and then all I'm doing is adding up all three of these numbers so 84 plus 60 7.2 plus fifty seven point six gives me 200 8.8 squared centimeters okay so everything this highlight here is exactly from this formula all right moving on to our last example geode is being sent as gift it is packaged in box that measures 7 inches long 3 inches wide and 16 inches tall what is the surface area of the box so once again long means length with me wide means width and then Tom means height and then using the formula I'm just gonna plug all the numbers that know in so my length is 7 and my height right here is 16 plus 2 times 7 which is my length times 3 which is my width plus 2 times 16 which is my height times 3 which is my width all right and then so once you multiply so that you multiply 2 times 7 gives me 14 bringing down the 16 plus 2 times 7 gives me 14 bringing down the 3 plus 2 times 16 gives me 32 times 3 and then they multiply 14 by 16 to get 224 multiply 14 by 3 to get me 42 and 32 times 3 gives me 96 once you add all three of these numbers up you should get 362 square inches okay and so I've highlighted everything here so sometimes it's better if you write it out clearly so you know exactly what numbers to substitute and plug in all right that's it boys and girls