[Music] welcome to math with mr j [Music] in this video i'm going to cover how to find the surface area of a rectangular prism and remember when it comes to surface area simply put it's the total area of the outside part or layer of a 3d figure so when it comes to rectangular prisms they have six faces so we need to find the area of each face and add all of that up in order to get the surface area now at the top of your screen in blue we are going to use that formula there in order to find the surface area of a rectangular prism so surface area equals 2 times front or back plus 2 times right or left plus 2 times top or bottom so let's talk about what that means now i have everything multiplied by 2 because for example if we pick the front or back let's say we pick the front here if we find the area of the front we can multiply that by two because the back is the exact same as the front same with right and left we can find the area of the right face and then multiply it by 2 because the left is the exact same as the right same with top and bottom so let's get into finding the surface area here and we'll start with surface area equals 2 and we need to find the area of the front or back so let's find the area of the front where we have a 6 by two so we can do area equals length times width for a rectangle plug in area equals six times a width of two and we get an area of 12 square inches for the front so we could plug in 12 here plus now we need to do the right and left now but before i get to that i want to mention to the right here i have a net of that rectangular prism so basically i unfolded it so you can see all of the faces and it's not in 3d form so it kind of lays everything out so we can visualize what we're doing a little better so as of right now we have 12 square inches here for the area of the front and the back so let's do right and left so we'll pick the right side here the right face and we have a three by two so area equals length times width so we can plug in three times two and that gives us an area of let's actually write it out length times width area equals 3 times 2 so that area is going to be 6 square inches so again that's the right and left so we would do 2 times 6 for the right and left and lastly we need to do the top and the bottom so we're going to take a look at the top where we have a six by three so area equals length times width plug in six times three and we get an area of 18 square inches so our bottom is 18 square inches and our top is 18 square inches so we would plug in 2 times 18. now let's start solving 2 times 12 is 24 2 times 6 is 12 plus 2 times 18 is 36. so the top or i'm sorry the front and back combined we have an area of 24 square inches the right and left combined area of 12 square inches and the top and bottom has a combined area of 36 square inches so we have all of our faces included now we just need to add everything together so surface area equals 24 plus 12 is 36 plus 36 gives us an answer of 72 square inches so that's the area of all of the faces added together so there you have it there's how you find the surface area of a rectangular prism again find the area of each face and then add all of that together i hope that helped thanks so much for watching until next time peace