How to Find the Surface Area of a Rectangular Prism Surface Area Partners in Prime

in this video I'm going to show you guys how we can find the surface area of rectangular prisms and if you look at the top of the screen we have this formula that says the surface area is equal to 2 * the length time the width plus 2 * the length time the height plus 2 * the width time the height so what want to start by doing first is actually just writing out which sides want to Define as the length the width and the height so I'm going to say the length is 10t the height I'll do width next the width is 4T and the height is 5T and technically it doesn't matter which sides you assign to the length the width and the height but think typically the horizontal line we're going to assign as length the vertical line we're going to assign as height and the other one is going to be our width and now want to show you guys visually why this equation works so when we're finding the surface area of any 3D shape what we want to do is just find the total area of all of the faces so I'm actually going to do that instead of using the formula and hopefully you guys can see where the formula comes from so what want to do first is find the area of the top and bottom and you may notice that the top and bottom are going to be the same so I'll put top here and then I'll put bottom here so the top of our shape is here and the bottom of our shape is down here and you may be able to tell that these are going to be the same rectangles so they're going to have the same area so to find the area of the top we are going to multiply our length of 10times our width of four so if we do that we're going to get 10 * 4 which is 40t and for the bottom we're going to do the same thing we're going to multiply our length of 10 by our width of four and if we do 10 * 4 again we get 40t and now you guys may understand that this is where this 2 * * comes from because we multiplied the length times the width to find the top and we multipli the length time the width to find the bottom so to find the total area of the top and bottom you're going to do two times the length times the width and we figured out that they're each 40 so Al together that's going to be 80t squ and now we're going to do the same thing for the front and the back take the front and we'll take the back so let me just erase what we did for the top and bottom so it's easier to see the front and the back so the front is going to be right here and the back is going to be this rectangle back here and you can probably tell that these are the same rectangles so they're the same size so they're going to have the same area so to find the area of the front we know that this bottom side is also Al 10 ft so we're going to have to multiply our length time our height and we know our length is 10t and our height is 5T and if we multiply those together we get 50t squar and now for the back we also know this height back here is 5T so again we need to multiply our length times our height which is going to be 10 * 5 which is going to give us 50t squar so now you guys may be able to tell that this 2 LW is going to come from the front and the back because to find the area of the front and the back we had to multiply length time height and we did that twice so it's 2 * length time height and we know that the front and the back are each 50t squar so if we add those together we're going to get 100t squar for the front and the back and finally we're going to do the same thing for the left and the right so let me just erase this and let's put this in we'll put this in yellow so the left side is over here and the right side is over here and you can probably tell that these are the same size rectangles so to find the area of the left side we're going to have to multiply the width times the height our width is 4T and our height is five and four * 5 is 20 so we get 20 ft squar for the left and for the right side we can fill in the side lengths we know that this down here is going to be 4et that's our width and this side is 5T which is our height so again we have to multiply the width by the height which is 4 * 5 again which is going to give us 20t squared so you can probably tell that this 2 wh comes from the left and the right because they're each found by multiplying the width by the height so we get 2 * * for the left and right sides and we know that each side is 20t squared so Al together it's 40t squ and now to find the total surface area which I'll do over here on the left so total surface area we're just going to add up all of those areas that we found for all six of our sides so we know that the top and bottom together are 80t squared we know that the front and back are 100t squar and we know that the left and the right are 40t squ and now we're just going to add these together and 80 + 100 is 180 and 180 + 40 is going to give us 220t squared as our total surface area so hopefully this video helped you guys understand how to find the surface area of rectangular prism you can either memorize this formula that says it's 2 * length time width plus 2 * length time height plus 2 * width * height or you can visually understand that you just need to find the area of all the different faces of this prism