4 Steps to Successfully Solve Area of Composite Figures

The Short Guide for finding Area of Composite Shapes

Area of Composite Figures Practice Problems Quiz

Watch the video explanation of our Area of Composite Figures Worksheet

Watch our free video on how to find Area Composite Figures. This video shows how to solve problems that are on our free Area of Composite Shapes worksheet that you can get by submitting your email above.

Watch the free Area of Composite Figures video on YouTube here: Area of Composite Figures Video

Video Transcript:

This video is about finding the area of composite figures. It will especially help you for 6th grade area of composite figures problems. You can get the Composite Area worksheet used in this video for free by clicking on the link in the description below. A composite figure is any figure that is made up of two or more different shapes. In order to find the area of a composite figure you have to break the composite figure up into different shapes that you can find the area of. In this example we have a composite figure that is made up of different shapes. We’re going to break this composite figure into rectangles so that we can find the area of each rectangle and then add them together. Typically, the shapes that you can use in order to find the area of composite figures are rectangles, triangles, and circles. The area of a rectangle is length times width so if you break a composite figure into a rectangle you can use this formula to find the area. The area of a triangle is base times height divided by two. Sometimes we say one half base times height and then area of a circle is pi times the radius squared. In the case of our example here we don’t have to use triangles or circles we can just use rectangles to break this figure into shapes that we can find the area of.

If you look we have one side that is 30 inches long we have another side that’s 12 inches long. This side right here is 5 inches and this bottom line is 10 inches long. What I’m going to do is I’m going to draw dotted lines to break the figure into two separate rectangles. I’m going to draw a dotted line right here across the middle and I’m going to label this rectangle one. And I’m going to label this one rectangle two. Now we have two separate rectangles in order to find the area of rectangle one. Rectangle one this is a rectangle so the area is length times width. That means we’re going to multiply 30 times 12 and get 360 inches. The area of rectangle 2 is also length times width and the length of this one is 10 inches and the width is 5. The area of rectangle 2 is 5 times 10, which would be 50 inches. In order to find the area of the entire composite figure you have to add the area of this rectangle plus the area of this rectangle. That means we’re going to take 360 because that’s rectangle 1 and add it to the area of rectangle 2 which is 50.  360 plus 50 is 410 inches squared. Our final solution will be 410 inches squared for this composite figure.

Let’s do a couple practice problems on our composite shapes worksheet. Number one on our area of composite figures worksheets gives us side lengths of 8 inches 2 inches 7 inches and 10 inches. It says to find the area of the composite figure. In the case of this problem the only shape that we need in order to find the area of this composite figure is a rectangle. We know the area of a rectangle is equal to length times width. When I find the area of this composite figure, I’m going to break it into two separate rectangles. I could draw a dotted line here and I could use this for a rectangle and this for the second rectangle or I could draw a dotted line here and use this for one rectangle and this for the other rectangle. Whichever way you do it, it does not matter as long as you use the correct side lengths. In order to find the area of rectangle one, I’m going to say area of rectangle 1. This is equal to length times width in the case of this rectangle we have a length of 8 inches. This is going to be our first length. 8 inches times the other side length which is 2 inches. 8 inches times 2 inches so the area of rectangle 1 is 16 inches and I’m going to say this is 16 inches squared. We know this is 16 inches squared the area of rectangle 2 is again length times width because it’s a rectangle this time the length of this rectangle is not 10 inches 10 inches goes from this side all the way to this side. It’s this whole distance right here. We’ve already used this distance from here to here and we’ve already used it in our first rectangle for two inches. We know this is two inches. We’ve already used this. We’ve already accounted for it that means from that dotted line all the way to this side. this has to be eight inches because we’ve already used two inches. this is two inches from here to here, this has to be eight inches from here to here, because the whole thing has to be 10 inches. Our length for our second rectangle is going to be 8 inches because we’ve already used 2 out of the 10 inches then the width is going to be 7 inches because this side we did not change. 8 times 7 is 56 and then in order to get the area of the entire figure you have to add 56 inches squared. The area of the second rectangle plus the area of this first rectangle. We’re going to say 16 inches squared plus 56 inches squared and we’re going to get 72 inches squared and we know the area of this composite figure worksheet is 72 inches squared.

The last problem we’re going to do on our composite figures area worksheet is number four. Our composite figure this time is made up of two separate shapes. We have a rectangle here this is a rectangle and we also have a triangle which is here. We’re going to find the area of the rectangle first and we’re going to find the area of the triangle second and then we’re going to add them together. We know area of a rectangle is length times width and we also know that the area of a triangle is base times the height divided by two. The first thing we’re going to do is find the area of this rectangle. Shape one is length times width. The length in this case is 24 inches and the width is 10 inches so we’re going to do 24 times 10 and we’re going to get 240 inches squared. We know shape 1 is 240 inches squared shape 2 is a triangle. We know that the area is base times the height divided by 2. The base in this case is the distance all the way across from one side of the triangle to the other so we know this distance is the same as this distance because it’s a rectangle. This whole side on the bottom is 24 inches that means the opposite side is also 24 inches. We know the base is 24 inches and they say the height of the triangle is 9 inches. We’re going to do 24 times 9 and get 216 inches and then to find the area of the entire composite figure. We have to add the triangle plus the rectangle. We’re going to add the rectangle which is 240 inches squared plus the triangle which is 216 inches squared the final area of the entire area of composite figures worksheet grade 6 is 456 inches squared. You can try all of these practice problems by downloading our composite figures worksheet with answers above.