Finding the Perimeter and Area of a Composite Shape L Shaped Example Geometry Math with Mr J

Welcome to math with Mr. In this video, I'm going to cover how to find the perimeter and area of composite shape. For our example, we will be working with an L-shaped figure. Let's start by finding the perimeter and then we will move on to finding the area. Remember, the perimeter is the distance around the outside of shape. We need to add all of the sides in order to find the perimeter of something. The first thing that we need to do is find any missing side lengths, if there are any, because we will need all of the side lengths in order to find the perimeter. For our example, we have two that are missing. This side and this side. We need to use what we know, so what we are given, to figure out what we do not know. For example, we know that this vertical side right here measures 11 ft. We can use that to figure out what this missing side equals. We know that this is 4 ft plus what will give us that 11 ft. Those two vertical sides need to equal 11 ft. Well, 4 ft plus 7 ft equals 11 ft. So, that missing side length equals 7 ft because again, we have 4 ft plus 7 ft gives us that 11 ft. Now, we can figure out this missing side length right here, so this horizontal side. Again, we need to use what we know, what we are given, to figure out that missing side length. So, let's use these two horizontal lines. Right here, we have 8 ft and we have 6 ft. Those two sides are going to equal that missing side length. So, we have 8 ft plus 6 ft gives us 14 ft. So, that missing side length measures 14 ft. Now, we can add all of the sides in order to find the perimeter. So, perimeter equals and will start with 6 ft here, so 6 plus and I'm going to cross off the sides as go around. That way, make sure don't forget anything or count anything twice. So, next we have plus plus plus 7. So, 6 plus 11 is 17 plus 14 is 31 plus 4 is 35 plus 8 is 43 plus 7 is 50. So, the perimeter equals ft. So, that's how we find the perimeter. Let's move on to finding the area. Now, remember, area is the amount of space or surface inside of shape. So, how much space or surface something covers. When we find the area of composite shapes, we can separate the shape into simpler shapes. We find the area of those shapes and then add them together to find the total area. Let's jump into our example and you'll notice we don't have simple rectangle, square, triangle, or whatever the case may be that we can easily find the area of. So, let's separate this shape or break this figure up into simpler shapes to work with. Now, there are different ways to separate this figure, but I'm going to separate it into top and bottom. So, let's separate this into top and bottom rectangle. Now, you can also separate this into left and right. Either way is correct and you will get the same total area in the end. Now, let's call this shape and this shape Let's start by finding the area of and since it is rectangle, let's use the formula area equals length times width. Now, I'm using cursive that way it doesn't look like one. Now, we need to find the correct length and width for rectangle Well, this is seven by six rectangle. So, let's plug those in. 7 times 6. It's very important that we pick the correct length and width for the given rectangle. For example, we don't need this 11 ft here. That goes all the way down here. So, be careful about which side lengths you are using for calculating the area. also want to mention, don't get too held up on which is the length and which is the width. I'm using the longer side length for the length to keep it consistent, but really, you're going to get the same area either way. So, in my opinion, don't get too held up on which is the length and which is the width. Just make sure you are using the correct sides for calculating that area. So, as far as the area for 7 times 6 gives us 42 and this is square feet. So, the area here is 42 square feet. Now, we need to find the area of So, area equals length times width. So, now let's pick out the correct sides here as far as what we need to calculate the area. This is 14 by four rectangle. So, 14 ft by 4 ft. So, let's plug those in. Again, I'm using the longer side length for the length. So, times 4. Now, before we multiply 14 times 4, do want to mention we did not need this 8 ft because that only goes to that point. We needed the 14 ft all the way across the bottom of that rectangle. So, again, we need to be careful as far as which side lengths we are using. So, now let's multiply. 14 times 4 equals 56. So, the area of is 56 square feet. Now, we have all of the information we need to find the total area of the composite shape. We need to add so 42 square feet, plus 56 square feet. So, the total area, we have 42 square feet plus 56 square feet. 42 plus 56 gives us 98 square feet and that's our final answer here, the final area of that composite shape. So, there you have it. There's how to find the perimeter and area of composite shape. hope that helped. Thanks so much for watching. Until next time. Peace.