Chapter 10 Lesson 3 Surface Area of Rectangular Prisms

chapter 10 lesson 3 surface area of rectangular prisms the surface area of rectangular prism is the sum of the area of all of its faces so the formula is surface area equals two times the length times the width plus two times the length times the height plus two times the height times the width example one find the surface area of the prism so this prism were given the net because it's opened up so we want to find the surface area by finding the area of each individual shape so if we start with this green box right here this green box has dimensions nine by seven so to find the area of the green box we do nine times seven which gives us 63 for that box this blue box has dimensions seven by five so we do seven times five to find the area of it which is 35 this box in the middle this side is the same length as this five right here so we know that this has dimension of five meters this side is the same size as this so know that this is nine meters and the area of this is nine times five which is 40 pipes down here we have green box that has dimensions seven and this is the same size as this and this and this which is all nine meters so the area of this is nine times seven which is 63 this blue box has dimensions seven and this is the same size as this over here so this is five seven times five gives us 35 and then we have this last box which is 9 meters by again this is 5 meters because it's the same size as this one here and 9 times 5 gives us 45 so now to find the total surface area we have to add up all of our areas so we have 35 plus 63 plus 45 plus 63 again plus 35 plus 45 so first we have 5 10 15 20 and then 23 and 26 next we have this 6 + 4 gives us 10 and this 6 + 4 gives us another tense that's 20 plus 3 more is 23 another 3 is 26 plus 2 more is 28 so our total surface area is 286 meters squared and remember that area is always units squared try this problem yourself to check for understanding example to find the surface area of the prism so we need to find the area of each part of the box so if we start with this part back here we have the dimension 5 and then this side is equaled to this so this side has dimension of 8 because it's the same as this side so here we can write 8 so the area of this is 8 times 5 which is 40 and because this is box we know that this side up here is going to be the same as that which is also going to be 40 next we have the order along the side here this area here has dimensions 5 by 13 so the area of this is 5 times 13 which is 85 and then we know that this side is going to be the same the last part is the bottom of the box and this has dimensions 8 by 13 which is 8 times 13 gives us 104 to find the total surface area we have to add up all the areas so on the bottom of the box we got 104 we have to add that twice because we also have the top of the box which is also 104 then we have 85 plus 85 and then we have 40 plus 40 so here we have 5 plus 5 is 10 plus another 4 is 14 plus another 4 is 18 then we have 8 plus 8 is 16 plus 4 more is 20 plus another 4 is 24 plus one more is 25 then we have 2 plus 1 plus 1 which is 4 so our total surface area is 458 inches squared try this one your self to check for understanding example three Heather is wrapping gift for her friend the dimensions are 9 inches long 10 inches wide and 13 inches tall to determine how much wrapping paper to buy she needs to find the surface area of the gift what is the surface area of the gift ok so let's try and draw gift box okay so we know that it's 9 inches long 10 inches wide and 13 inches tall so let's find the surface area by finding the area of each piece so this piece here in the back is going to be 13 by 10 so 13 times 10 gives us 130 and then we know that the front piece is also going to be 130 next we have the side piece here which is 9 by 13 so 9 times 13 which is 117 and then we know this piece is also going to be 117 lastly we have the bottom piece and this bottom piece is 10 by 9 which is 90 and then we know we also have the top of the box which is also going to be 90 so we have 90 twice for the top and the bottom then we have 130 twice and then we have 117 twice so let's add them all up to find the total surface area so 7 plus 7 gives us 14 then we have 9 plus 1 is 10 9 Plus this one is another 10 so that's 20 20 plus 3 is 20 3 plus 3 more is 26 plus one more is 27 then we have 2 plus 1 2 3 4 which gives us 674 so our surface area is 674 inches squared pause the video here and try this one yourself to check for understanding