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

In this video, I'm going to cover how to find the perimeter and area of a 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 a 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 feet. We can use that to figure out what this missing side equals. We know that this is 4 feet plus what will give us that 11 feet. Those two vertical sides need to equal 11 feet. Well, 4 feet plus 7 feet equals 11 feet. So that missing side length equals 7 feet, because again we have 4 feet plus 7 feet gives us that 11 feet. 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 feet and we have 6 feet. Those two sides are going to equal that missing side length. So we have 8 feet plus 6 feet gives us 14 feet. So that missing side length measures 14 feet. Now we can add all of the sides in order to find the perimeter. So perimeter equals and I will start with 6 feet here. So 6 plus 11 and I'm going to cross off the sides as I go around. That way I make sure I don't forget anything or count anything twice. So next we have 14 plus 4 plus 8 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 50 feet. 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 a 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 a 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 a top and a bottom. So let's separate this into a top and a bottom rectangle. Now you can also separate this into a left and a right. Either way is correct and you will get the same total area in the end. Now let's call this shape A and this shape B. Let's start by finding the area of A. And since it is a rectangle, let's use the formula area equals length times width. Now I'm using a cursive L, that way it doesn't look like a 1. Now we need to find the correct length and width for rectangle A. Well, this is a 7 by 6 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 feet here. That goes all the way down here. So be careful about which side lengths you are using for calculating the area. I 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 A, 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 B. 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 a 14 by 4 rectangle. So 14 feet by 4 feet. So let's plug those in. Again, I'm using the longer side length for the length. So 14 times 4. Now before we multiply 14 times 4, I do want to mention we did not need this 8 feet. Because that only goes to that point. We needed the 14 feet 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 B 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 A, so 42 square feet, plus B, 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 a composite shape. I hope that helped. Thanks so much for watching. Until next time, peace.