Finding the Area of a Composite Figure Area of Composite Rectangles

Welcome to Math with Mr. In this video, we're going to talk about how to find the area of 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 mean by that. So, for number one, the first thing want to do is again separate into simpler shapes. So, I'm going to cut this into two rectangles. And I'm going to draw dashed line here to represent where I'm cutting it. Now, I'm going to name the left rectangle and the right rectangle And it's going to that's going to help keep me organized as work through this problem. So, know that finding the area of rectangle, area equals length times width. So, now, let's find the area of our rectangle and rectangle So, and So, area equals length times width. All right, now need to plug in length and width. So, my length for 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 area equals 24 square inches. Now, let's do Area equals length times width. Let's plug in. Length is going to be this 2 inches here. So, two 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 * 7 square inches. So, the area for 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 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 top and bottom rectangle. So, usually there's multiple ways to separate 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 little more complex. Now, for this one, I'm going to cut it into or separate it into three simpler shapes here. And have two rectangles and square. So, I'm going to name and 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 our length is going to be this five all the way up. So, we have 5 cm. times the width of 2 cm. And that gives us an area of 10 square centimeters. So, let's do Now, we have length of right here or right here, and we don't have measure there. So, we're going to need to figure it out. So, we know the whole shape is 5 cm, right? So, if we have this three, what's this going to have to be in order to get us to that 5 cm? Well, it's going to have to be 2 cm. And again, figured that out because this three right here plus this 2 cm equals the total height of the 5 cm 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 3 cm, which is given. So, 2 * 3 gives us six square centimeters. And lastly for we have square here, 5 * 5 square. So, our length is five and our width is five. So, our area is going to be 25 square centimeters. So, now we need to add these together. 10 + 6 + 25. 10 + 6 is 16 plus 25 is going to give us 41. So, the area, I'm going to put it in the top right corner where 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.