6 th Grade 10 3 Surface Area of Rectangular Prisms

chapter 10 lesson 3 surface area of rectangular prisms you will be able to find the surface area of rectangular prisms the surface area sa of rectangular prism with length width and height is the sum of the areas of the faces so if we were to take this rectangular prism and unfold it we would see this two-dimensional figure now with rectangular prism it has three sets of congruent sides so these two sides would be congruent the bottom and the top would be congruent and the back and the front would be congruent so to find the surface area what we need to do is find the area of each different face there are three different faces we have one here one here and one here now the blue faces are the same the green faces the same and the peach faces the same so let's find the area of one it is rectangle so the area is base times height the base and height are six and seven which is 42 now remember there are two of them so I'm going to take that amount and multiply it by two and get 84 for the blue on to our second one the green it's also base time height because it's rectangle it's base and height are 8 and six 8 * 6 is 48 again there are two of these rectangles so multiply by two and we get 96 our last rectangle it's also base time height now we have this height which matches 7 and this base which matches 8 so 8 * 7 which is 56 again times 2 and we get 112 all we need to do then with these three areas is add them up 112 90 86 and 84 so our total surface area is 292 squared letter here's one rectangle second rectangle and third rectangle and remember these match up with their corresponding opposite side so area of one base times height which is 10 and 10 10 * 10 is 100 there are two of them so multiply by 2 and the blue faces are 200 onto the green faces also rectangles area equals we have our base and height is 15 and 10 so 15 * 10 is 15 and there are two of them so multiply by two and we get an area of 300 our third rectangle we have base matching 15 and height matching 10 multiply together we get 150 there are two of them and we get 300 add up those areas is 200 300 and we get total area of 800 in squared now we can also use formula to find the surface area of rectangular prism since there are two of each side that's why we have these twos in our formula we multiply 2 * the length and width 2 * the length and height and two * the width and height so here's our rectangular prism we'll just label length width and height our formula surface area equals two length width plus 2 length height plus 2 width height plug in everything you know so surface area equals 2 * the length of 5 times the width of 7 + 2 times the length of five time the height of four + 2 * the width of 7 time the height of four surface area equals 2 * 5 * 7 is 70 plus 2 * 5 * 4 is 40+ 2 * 7 * 4 is 56 add those amounts together we have 70 + 40 + 56 we get total area of 166 ft squared okay let's mark seven as our length 4.8 as our width and six is our height it really doesn't matter on rectangular prism what your length width and height are surface area equals 2 * length * width + 2 * length * height + 2 * width time height plug in your values surface area equals 2 * 7 * 4.8 + 2 * 7 * 6 + 2 * 4.8 * 6 surface area equals 2 * 7 * 4.8 is 67.2 + 2 * 7 * 6 is 84 plus 2 * 4.8 * 6 is 57.6 add those amount amounts together and you get surface area of 28.8 cm squared find the surface area of the rectangular prism length width and height surface area equals 2 * length * width + 2 * length * height + 2 time width time height surface area equals plug in your values 2 * 3 * 4 + 2 * 3 * 2 + 2 * 4 * 2 surface area equals 2 * 3 * 4 4 is 24 + 2 * 3 * 2 is 12 plus 2 * 4 * 2 is 16 add those up and we get total surface area of 52 squared letter 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 there we have our length width and height surface area equals 2 * length * width + 2 * length * height + 2 * width time height plug in your values 2 * 7 * 3 + 2 * 7 * 16 + 2 * 3 * 16 surface area equals 2 * 7 * 3 is 42 2 * 7 * 16 is 224 and 2 * 3 * 16 is 96 add those up and we get surface area of 362 Ines squared