How To Find The Area of Composite Figures Using Rectangles Prealgebra

in today's lesson we're going to talk about how to calculate the area of composite figure and we're going to do so using rectangles so just to recap let's say if we have rectangle with the length and the width the area of that rectangle is length time width so for instance let's say we have rectangle that's 5 in long for in wide the area is going to be 5 * 4 which is 20 square in so that's how we can calculate the area of rectangle but now let's apply that to the composite figure that we have on the screen now what we want to do is we want to break apart this figure into smaller rectangles and one way we could in which we could do that is we can draw line so I'm going to draw line here and separate it into two parts so we'll call this rectangle one and this one rectangle two now for rectangle one we could see that the area is well rectangle one has the length of four and width of six so if we multiply length time width 4 * 6 that will be 24 square cm so that's the area of the first rectangle now for the second rectangle we can see that it has length of 11 and width of four so 11 * 4 that's going to be 44 now to get the total area of the composite figure we simply need to add the two areas of the smaller rectangles so it's 24 + 44 and that's going to be be 68 square cm so that's the area of this composite figure now it doesn't matter how you break up the composite figures into smaller parts the answer will still be the same so for instance let me just undo what did let's say if we decided to break it up this this way so the first rectangle on the left we can see that it has length of four width of 10 4 * 10 that's going to be 40 square cm and then for the second rectangle it has length of seven width of four so 7 * 4 is 28 if we add up 40 and 28 we will still get the same answer 68 sare so it really doesn't matter how you decide to break up the composite figure your answer should still be the same now let's move on to our second example this one is going to be little bit harder than the previous one so if you want to try this problem feel free to pause the video and work on the example so let's begin by breaking up this composite figure into smaller rectangles what I'm going to do is I'm going to put line here and here so we have three rectangles of which we need to calculate the area for now notice that this side is nine that means this side here has to be 9 in so for the rectangle on the left we have length of three width of 9 3 * 9 is 27 Square in now for the rectangle on the right we can see that we have length of four width of 9 4 * 9 is 36 so this is 36 square in now for the rectangle in the middle we have length of five but we don't know what the width is now if this part here is 9 in and this is 6 in how long should this side be well it's going to be the difference between 9 and six 9 - 6 is three since these two sides here they have to be equal so make sure you understand that so I'm going to put the three inches here so this is 3 + 6 which adds up to nine they they have to be the same length so now we could find the area of of the middle rectangle we have length of five and width of three so 3 * 5 that's going to be 15 Square in so to get the total area we're going to add up the individual values so we have 27 + 15 + 36 so the answer is going to be 78 square in so that's how we can calculate the area of this particular composite figure now for those of you who want to find other related content feel free to check out the links in the description section below so you can find it by clicking on more and have other videos like how to find the area of trapezoid parallelogram Romus kite an equilateral triangle and also how to find things like volume surface area of rectangular prism triangular prism and other shapes so feel free to take look at this when you get chance for those of you who are interested in that now let's move on to our third example go ahead and take minute and find the area of this composite figure now before breaking it up to rectangles what like to do is find the missing side LS so let's focus on this part here so that segment is 5 + 6 that segment is 11t long if we were to add these two side lefts and that should equal this side segment here which is also 11 ft now this part is 8 so what is this part here this unknown sign left it has to be the difference of 11 minus 8 so that has to be three so this is three feet now how can we determine this side length here so notice that this is three this is seven so that gives us total of 10 now this part over here is four units long or rather 4T long and this part should also be 10 they're the same so 10 minus 4 will give us this portion which is six so that's how you could find the missing side LS so if you wanted just to recap what we did quickly to get this part all we did was 5 + 6 which is 11 minus 8 that gives us three now for this part it's 3 + 7 which is 10 - 4 and that gives us six so that's just quick way that you know you could use to find missing side length so now let's break this up into smaller rectangles so I'm going to put line here and here so the area for the bottom rectangle we have length of four width mean length of eight and width of four 8 * 4 is 32 so this is going to be 32 square ft for the rectangle on top we have length of six width of Three 6 * 3 is 18 so we have 18 square ft now let's focus on the middle rectangle so we need to find the length and the width of that rectangle how can we do that so notice that this side length is 8T and this part is five 8 minus 5 will give us the remaining part here which is three so this is 3 ft now I'm going to color code that now what can we do to find this side left notice that this part is six and this is Three 6 minus 3 will give us this side length which is also three so we have length of three width of three 3 * 3 is 9 Square ft so the total area is going to be 32 square ft plus 18 square ft + 9 32 + 18 is 50 50 + 9 is 59 so the total area is 59 square ft now let's move on to our next example how can we find the area of this composite figure well like before let's find the missing side lengths so this side is four and and this side is 9 if we add four and 9 it will give us the length of this side which is going to be 13 now notice that this is 15 and this part is 12 using subtraction we can get this side length which is going to be 15 - 12 and that's going to be three so this is 3 cm and this side is 13 cm so now we have everything that we need to find the area so let's break this up into two rectangles I'm going to put line right here so for the first rectangle we have length of 12 and width of 13 so multiplying 12 by 13 that's 156 square cm now for the smaller rectangle on the right we have width of nine length of three so 3 * 9 that's going to be 27 and square cm so the total area is going to be 56 square cm plus 27 squ which will give us total of 183 square cm so that's it for that example that's basically it for this whole video so now you know how to find the area of composite figure using rectangles