 Hi, this video is called Find the Area of the Shaded Region 2. If you look at this picture, it is extremely similar to the picture of the problem we just completed, but I promise you it will take us a lot less time to get this problem done. Look at this problem. Look at the one you just did. The pentagon is exactly the same. Well, let me back up. What's different about the problem is that this time the circle is inside the pentagon instead of outside the pentagon. But if you look, the pentagon is exactly the same. It has a side length of 6. So to find the area of this shaded region, we'll have a very similar approach. Always do the bigger shape or the shape on the outside minus the smaller shape or the shape on the inside. So this time our setup will be the area of the pentagon minus the area of the circle. So we have two things we need to figure out here, and once we have them, we can subtract and simplify to get our answer. Well, let's take a little bit of a shortcut. Because we recognize that we have the exact same pentagon, it will have the exact same area. And we already found that in the last problem. So if you look at the last problem, you can see the area of your pentagon was 61.9. Let's just go ahead and put that in. So it looks like all the work we have to do in this problem will be finding the area of the circle. Once we have that, we'll be able to subtract and we'll be set. Hopefully you can remember, to find an area of a circle, you do pi times the radius squared. So if we can just figure out what the radius is, we can plug it into our calculator, square it, multiply it by pi, and we'll be all set. So look at this picture, be really very careful when you look at what the radius is. From the center of that circle, I see a dotted line and I see a solid line. The dotted line looks like it's the radius of the pentagon because it goes out to the corner. But the solid line here, that's the one that goes from the center of the circle to the edge of the circle. Can you see how this dotted line, it goes past the edge of the circle to hit the corner of the pentagon? It's too long. That is not the radius of our circle anymore, where the solid vertical line here is. Look back at the last problem. What was that solid vertical line? It wasn't the radius, but it was the apathome or apathome of my right triangle. So if you look back on your notes from the last problem, you would see that your apathome was 4.129145 before you rounded it. So again, at this point, it would be way too early to round that to 4.1. So what you're going to have to do is punch that big number in your calculator. I know it'll take a second, but I think you can handle it. 4.129145. Then in your calculator, hit the exponent of two button and press equal. That is going to give you, gosh, I don't even, I don't even know. It'll be 4.129145 squared, press equal, then press the pi button, press equal again, and it'll give you 12.972. I have to apologize. Let me back up. I've been doing my math wrong. So let's just slow down a little bit. In your calculator, when you do 4.129145 squared, you get 17.04983843. At this point, it's still too early to round. Let's go ahead and multiply it by the pi button. So hit, in your calculator, you've got this long number in your calculator. Hit times, use the pi button, don't use 3.14, and press equal. So you're going to get another big, long number. It's 53.56464716. At this point, because it's the area of the circle, let's go ahead and round. So this five, you look at what comes after it. Since it's a six, we will round it up to 53.6. So the area of my circle is 53.6. Now, the only thing left to do is to subtract. 61.9 minus 53.6 gives me 8.3 units squared. So the area of the shaded region was I took the area of the pentagon, which we found in our last problem, subtracted the area of the circle, which I just found here, and I got 8.3 units squared.