 Hi, this video is called Find the Exact and Approximate Area of the Shaded Region 2. If you take a look at this picture, you can see a square. You can see a circle. And you can see that the circle is inside of the square. So the square is the bigger object. So to find the area of the shaded region, you'll do the area of the square minus the area of the circle. So if you can imagine a big square with paper, construction paper, and someone cut out a circle. And so what's left of that construction paper is what you're looking for. So I have two pieces I need to find. Once I have them, I can start simplifying. So if you look at this picture, let's think about this. Area of a square. Well the formula for that is easy. It's side length squared. So if I can get one of those side lengths, I'll be all set. The area of the circle is pi r squared. So if I can get my radius, I will be all set. All right, so I'm set up with my formulas. I see the approach I'm going to take. Now it's time to figure some stuff out. Look at the one piece of information they give us from the center of the circle and the center of the square all the way out to the edge of my square. Well that's not the radius of my circle. It's too long. It goes past the circle. It would be considered the radius of the square. So we might as well start by figuring out what the area of the square is. Since the square has four sides, you can draw in 4 radii. 360 divided by 4 is 90. So you know all of your central angles are 90 degrees. But I think on that bottom triangle, I'm going to drop down the apathome. And that 90 gets cut in half to a 45 and a 45. Got a 90 here. So if we look at this, I'm going to take this. A triangle right here. Recognize I have a 90. I have a 45 and a 45. And that this right here is 5 root 2. Well I'm glad it's a special right triangle. That makes it easier for me. Opposite the 45 is N. Opposite the 45 is N. Opposite the 90 is N root 2. So if 5 root 2 equals N root 2, to get that N alone, we can divide both sides by square root of 2. They cancel on both sides and N equals 5. So down here is 5 and my apathome is 5. Well I'm feeling pretty excited because if this is 5, that would be this on my picture. So then my entire side length of my square is 10. And that's what I need to find an area of a square. You need a side length. Side length is 10. 10 squared is 100. So the area of my square is 100. Now let's go ahead and deal with the circle, finding area of a circle. Well I actually think, I'm feeling pretty good about this, I actually think I did the work. This right here, we found to be 5. In my picture, that's the radius of my circle. It's the apathome of the triangle, but it's also the radius of the circle because it goes from the center to the edge of my circle. So I have a radius of 5. Well 5 squared is 25. So the area of my circle is 25 pi. So I look, 100 minus 25 pi, they're not like terms. The 100 would need a pi behind it to be like terms. So I can't do anything else. So I simply write a unit squared. And that is going to be the exact area of the shaded region. We didn't do any rounding, it stayed exact. Now to do the approximate, we are going to do some rounding. Well the 100 stays 100. If I do 25 times the pi button in my calculator, I get 78.5, what do I get? 398. And so when I subtract 100 minus that 78, that long number, I get 21.46018. And at this point, I can round. To round to the nearest 10th, we look at this 4, look at the number after it. If it's a 5 or above, we round up. Since it's a 6, we certainly do round up to 21.5 units squared. So that would be the approximate area of the shaded region because I rounded.