Grade 6 course 1 chapter 10 lesson 3 surface area of rectangular prism

in chapter 10 lesson number three surface area of rectangular prism Roberta is rubbing gift for her sisters foreign she places it in box with the measurements shown then length tin width and thin height what is the area of one face of the box one face of the box shaped like square so square is side times itself or length time times width so we say 10 multiplied by 10 equals 100 inch Square because it's an area how many faces does the Box have the books has six faces top and bottom front and back face to the right and face to the left so six faces what operation would you use to find the surface area of the Box surface area of the Box means all faces so multiplying six faces times the area of One Piece which is hundred this will give you six hundreds in square so the idea of the surface area of prism surface area of rectangular prism is to find the area of all phases the front and the back and the top and the bottom and the right is and the left face and so on let's go deep in the lesson for details surface area of rectangular prism this is the rectangular prism it has length and width and height the surface area means the total surface area of the prism means all faces all faces this is the rule you need to remember the rule it's two faces two phases like the front and the back times so 2lh plus another two phases the top and the bottom so LW and another LW to LW Plus another two phases the right face and the left face so two hcw or wh the same so 2lh plus two LW plus two or if you remember this cycle length width and height and make three arrows this way so you remember that length should be multiplied by widths length should be multiplied by widths and widths multiplied by height and height of the height by length and all of them should be multiplied by two in front of them so if you flatten if you flatten means you unbox the rectangular prism into this flat surface so we'll have this yellow part that is top and bottom this is the top and the bottom and you have the blue side faces this is the side face to the left hand side face to the right and you have the front and the back the green faces this is the front and the deck as you can see so the bottom always it has sides to the right and left and the front and the back will be up and down when you flat them when you flatten the Box and exactly the same as the bottom will be the top here to the very far right of the figure so moving on how can we find the surface area of this flat in the face so focus with that green part the front and back it will be six times eight another six times eight so we can say six times eight times two which is 2 by 48. now focus on the top and bottom the yellow ones of course you can get Dimensions easily this one is seven for sure like this one seven and this one is eight for sure like this one is eight so seven by eight times two seven by eight times two two times fifty six and the sides the blue Parts six by seven times two and you can add them all to find out it's 292. so it's related to the area related to the area listen means you need to go back and revise the area in chapter 9. now how can we find out this part very easy and you can find it here on the figure itself so look at the Blue Bar this is 10 by 10 so will write here 100 also this blue one will be 100 the same now let me take this green bar green part 15 times 10 will be 150. so this one will be 150 the same now this yellow part this one is 15 and this one is 10. this is 15 and this is 10 so also 150 and this one is 150 as well so we can say that the surface area will be two times the front and the back plus 2 times 150 the Euro Parts the top and the bottom Plus 2 times 100 the side faces this will give 300 plus another 300 plus another 200 so this will give 800. inch squared because this is an area 100 inch square as it's an area now the same is happening here to find the area of each face let's determine the dimensions the length is 7 and the width is 4.8 it really doesn't matter which one is the length and what but let's say that this is and this is and the height is six so front and back to LH equals two times seven times six of course 7 times 6 is 42 and 42 multiplied by two will give you 84. 2lw so 2 times 7 times 4.8 of course 2 times 7 will give you 14. and 14 times 4.8 this will give you 67.2 HW so 2 multiplied by 0.6 multiplied by 4.8 2 multiplied by 6 is 12. 12 multiplied by 4.8 this will give you 57 .6 now this is 84 plus 67 .2 plus 57 .6 84 plus 67.2 plus 57 .6 this will give you 28.8 Square centimeter square centimeters because this is an area problem find the surface area of rectangular prism let's write down the rule surface area equals to length width plus 2 what height plus 2 height length as told you length with height so length width what's high and height length and don't forget we multiply by 2 for each so let's see it's like 2 and 3 and 4. so we can say that the length is three and the width is 4 and the height is 2 all of the meter so three times four then four times two then two times three don't forget these two so 2 multiplied by three times four plus two multiplied by four times two plus two multiplied by two times three of course according to Pim desul we finish multiplication first then we will do the addition three by four twelve times two twenty four times two eight eight times two sixteen two times three six times two twelve 24 plus 16 is 40 plus 1252. 52 what meter squared because this is an area surface area it's an area so squared units in example number four as youth is being sent as gift it's packed in ebooks that measures 7 inch long three inches wide steam inch stole so Syrian 3 16. so 7 will be multiplied by three and three will be multiplied by 16 and 16 will be multiplied by 7 and every multiplication we have multiply by 2. so two length widths plus two length height plus two height weight so two multiplied by seven by sixteen plus two by seven by three plus two sixteen by three and you find out them all and you will have your final answer don't forget to write square inches or inch square let's find out the surface area of figure number one here in this blue part it has length and width 2 and 2.4 so multiply 2 times 2.4 this will give you 4.8 so this blue part is 4.8 as well now let's find this green part the green part will be 3 times 2.4 will give you 7.2 and this is 7.2 as well now this yellow part this year report it has length and width of 2 meters and three meters this one is two the same as this one and this one is three the same as this one so two multiplied by three will give you six and this one is six as well so final answer is like you are multiplying the blue Parts 2 multiplied by 4.8 plus 2 multiplied by the green part 7.2 plus 2 multiplied by the Yellow Part which is six two times four point eight will give you 9.6 2 times 7.2 will give you 14.4 2 multiplied by 6 this will give you 12. 9.6 plus 14.4 this will give you 24. 24 plus 12 will give you 36. so 36 meter squid Now problem number two we have lengths and widths and height so let's say that this is the height and this is the length and this is the word so they will say is surface area equals to length width plus 2 with the height plus two height length so 2 multiplied by length times width 5 times 10.25 Plus 2 times width times the height so 10 point 25 multiplied by 6.5 Plus 2 times height length so it's 6.5 multiplied by 5. and this will be of course 2 multiplied by 5 is 10 and 10 times 10.25 will give you 102 .5 Plus 2 multiplied by 10.25 times 6.5 2 times 6.5 is 13 and 13 times 10.25 this will give you 100 33.25 2x5 is 10 and 10 times 6.5 is 65. now we are going to add all these numbers 102.5 plus 133.25 plus 65 this will give you 300 points 75 feet Square and problem three the same rule surface area equals to length width plus two with the high plus two height length so let's say that the length is 15 and width is 7 and the height is two so this will be two times length width 15 times 7. Plus 2. what side seven times two plus two height length to multiply by 15. 2 multiplied by 15 is 30 30 by 7 2 times 2 is 4 by 728 2 by 2 is 4 by 1560 210 and 60 270 and 270 plus 28 will give you 200 centimeter Square because this is an area surface area it's an area the lesson is very easy just apply the rule remember the rule apply the rule very well know what is the length and width and height and that's it just substitute and calculate you are all excellent in calculations if it comes to you this flatten one find the blue it will be the same as the blue the green will be the same as the green there will be the same as zero then add them all and that's it Thomas keeps his the cast cars and glass display case as shown what is the surface area of the glass including the bottom means all of it all of it surface area surface area surface area sounds the same length width and high so surface area will be two times 15 multiplied by six plus two times six multiplied by 5 plus 2 times 5 multiplied by 15. 2 times 15 is 30 times 6 180 plus 2 by 5 by 6 will give you 60 plus two by five by fifteen one hundred fifty so this is 180 plus 60 will give you 240 plus 150 390. 390 watt inch square that's it for our lesson for today if you have question you can write it down in comments or you can raise you