Finding the Area of Composite Figures with Triangles Math with Mr J

Welcome to Math with Mr. In this video, I'm going to cover how to find the area of composite figures involving triangles. And we have two examples that we're going to go through together in order to get this down. Now, before we start, want to mention that we're going to separate these figures into simpler shapes. So, we're going to break them down into simpler shapes that we know how to find the area of, combine those areas to get the total area of these composite figures. So, let's jump right into number one here, where we have something that kind of looks like the outline of house. So, the first thing we need to do, again, is separate into simpler shapes. So, I'm going to cut this shape right here. And I'm going to label the top triangle and the bottom rectangle here So, we know how to find the area of triangle and rectangle, so we need to find the area of and add those together, and we have the total area of that composite figure. So, labeled them and to keep everything organized here. So, let's start with So, I'm going to put an over here. And our formula for the area of triangle, area equals base times height divided by two. Now, you may use 1/2 * base * height for the area of the triangle. That will give you the same answer. dividing by two is the same as multiplying by half. So, let's plug in. Area equals the base of right here, is 7 ft times the height, 3 ft, and divide by two. So, that gives us 21 divided by two. So, area equals 10 and 1/2 square feet. So, now we need to do So, area of rectangle, length times width. Let's plug in. Our length is 7 ft times width of 3 ft. Now, if you did 3 * 7, that would give you the same answer. So, don't get caught up on the length and width there. Area equals 21 square feet. So, now that we have the area of and we need to add those together for the total area of the composite figure. So, I'm going to come up here. Area's going to equal that 10 and 1/2 square feet plus the 21 square feet. So, let's add those together. 10 and 1/2 + 21 is going to give us 31 and 1/2 square feet. So, that's the total area for number one. So, let's move to number two here. Again, we need to separate into simpler shapes. So, let's cut this shape right here. That way we have triangle and rectangle. We'll call the rectangle and the triangle Doesn't really matter which one you name or or what you name them, as long as you're organized, and it will all work out in the end to give you the same answer. So, let's find the area of first. So, formula for rectangle, length times width. So, let's plug in. Length, I'm going to use Don't use the 15 ft. The 15 ft goes all the way across. We just want this 10 ft here. So, 10 times four, and the area's going to be 40 square feet for the rectangle. So, let's do the triangle Area equals base times height divided by two. So, let's plug in. So, we need this base here. It's not going to be 15. 15 goes all the way across, so we need to do some thinking here to figure out what that's going to be. So, it goes all the way across 15, so we need just this section here. So, we need to use what we have. We have 10 here. So, 10 plus what will give us that full 15? We can think of it as. So, this is actually going to be 5 ft. So, 5 times the height, which isn't labeled, but we can look over here at our four. So, the height is four, and we divide by two since it's triangle, and that's going to give us 20 divided by two. So, 20 divided by two is going to give us total area of 10 square feet. So, now that we have the area for and add them together for the total area of the composite figure. So, I'm running out of room here, so I'll go to the middle bottom of the screen here. So, area equals 40 square feet plus 10 square feet, and that's going to give us total area of square feet. So, again, added part and together for the total area of that composite figure. So, hope that helped. Thanks so much for watching. Until next time, peace.