welcome to math with mr. J in this video we're going to talk about how to find the area of a composite figure and on your screen there we have number one and number two and those are both examples of composite figures so what we need to do in order to find the area of these we need to separate them into simpler shapes that we know how to find the area of that way we can find the area of the simpler shapes add them together and it will give us the area of the whole composite figure so let's jump right into number one and see exactly what I mean by that so for number one the first thing I want to do is again separate into simpler shapes so I'm going to cut this into two rectangles I'm going to draw a dashed line here to represent where I'm cutting it now I'm going to name the left rectangle a and the right rectangle B and it's going to that's going to help keep me organized as I work through this problem so I know that finding the area of a rectangle area equals length times width so now let's find the area of a rectangle a and rectangle B so a and B so area equals length times width all right now I need to plug in lengthen width so my length for a is going to be this eight all the way up right don't use this six because this six doesn't go the full length of the rectangle so you have to be careful which measurements you use so I'm going to use the eight and I'm going to multiply it by the width of three and that gives me an area of 24 square inches so the area of a area equals 24 square inches now let's do B area equals length times width let's plug in length is going to be this 2 inches here so 2 times the width of 7 inches do not use the 10 the 10 goes all the way across we only want right here which is that 7 inches so area equals 2 times 7 14 square inches so the area for B is 14 square inches so now that we have the left rectangle and the right rectangle the area of those we add those together in order to get the area of the whole shape so we would do 24 plus that 14 and that gives us an answer of 38 so our final area is 38 square inches so again we separated into simpler shapes and then found those areas added them together for the area of the whole composite figure now for number one we could have cut that this way as well and made a top and a bottom rectangle so usually there's multiple ways to separate a composite figure it doesn't matter which way you separate it but it does matter which numbers you use which dimensions you use going around for your length and width so that's something you need to be careful of so let's jump into number two here and see how we do this one this one's a little more complex now for this one I'm going to cut it in two or separate it into three simpler shapes here and I have two rectangles on a square so I'm going to name a B and C so let's find the area of these three so area equals length times width I'll put my formula first and then what we will plug in so for a our length is going to be this five all the way up so we have five centimeters times the width of two centimeters and that gives us an area of 10 square centimeters so let's do B now B we have a length of right here or right here and we don't have a measure there so we're going to need to figure it out so we know the whole shape is five centimeters right so if we have this three what's this going to have to be in order to get us to that five centimeters well it's going to have to be two centimeters and again I figured that out because this 3 right here Plus this 2 centimeters equals the total height of the five centimeters given to us on the left and right hand side so sometimes in composite figures you have to figure out some measurements that aren't given so our length is going to be two times the width of three centimeters which is given so two times three gives us six square centimeters and lastly for C we have a square here five by five square so our length is five and our width is 5 so our area is going to be 25 square centimeters so now we need to add these together 10 plus 6 plus 25 10 plus 6 is 16 +25 is going to give us 41 so the area I'm going to put it in the top right corner where I have some room area equals 41 square centimeters and that's our final answer for number two now just like number one there's multiple ways to solve for that answer but again what's most important is picking out the correct measurements for your lengths and widths thanks so much for watching until next time peace