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Find the area of the shaded region.(Diagram Cant Copy)

$(\pi-1) \frac{25}{2}$ in $^{2}$

Geometry

Chapter 11

Circumference, Area, and Volume

Section 2

Areas of Circles and Sectors

Area and Perimeter

Surface Area

Volume

Circles

Piedmont College

University of Nottingham

Utica College

Lectures

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Yes. This is a cool problem. I like one. Um, we have a circle, and we find the shaded region in it. But there's a triangle. Tracked him from it. We're told that this night here, it's firing. Right. Um, we're also I think this is implicitly this here, uh, screen, like to draw is the radius, um, of circle. It's also the height of the triangle. You have to find area of the circle and the area of the triangle. Um, so ordered who find the final radius first. And that will become clear. Why? Since we write down the equations for the circle in the tribal, the area of the circle area of the circle equal to pi r squared. It's like it has been all doctor and then area of the triangle. It could be 1/2. I'm the base times height, 1/2 times the case times. He was a cool thing, though, Um, that's that's the center of circle. There. The point here on the basis of height or both. The radius. Um, where's pretty red? So this is gonna be on 1/2. Uh, I'm the radius times the radius. That's gonna be just the radius squared. But that's assuming that they're trying more and realistically. Sorry. That's Syria's one triangle. And there are two. Right, There's the left, one in the right one So we can actually get rid of that 1/2. Well, it's just kind of strike that out. Oh, great. Okay, so now the total area. Good day. Um oh, Sorry. Well, area that's his area of the circle that is not inside the triangle. The total area is in the area of the circle my ass area of a triangle. I r squared minus R squared. Right. So that his high manage one r squared. And now we really need to figure out Miss, um, these are Okay. So this plan writes one r squared. That's about a simple That could go. I was finding that actual radius. Um, but to do that with it, remember, son? Um um uh, things about 45. 45 90 triangles. We've got a 90 degree there. What? 90 degrees there? Andi, he's reached 45 degrees. Um, so we're we're under our, um Our rules about hungry for our, uh are 45 45 90 tribal. Do you have a triangle like that. It was just a blown up version. Um, of that. Try and go over there. Um, side lee are in ratio of one. Do one to root. Do. Right. Um, it's just one of things you have to have memorized from trigonometry. If you don't have memorize to use appropriate, memorize it. It's very, very useful. That will be useful for future. Um, so in our case, we have a five right here and not want to know what radius is. Radius is regular, but we can analyze that and say, OK, radius. Um, here, the radius is then going to be equal you, but okay, I'll be more explicit about it. So the ratio of whoa. Okay. Radius Who won nickel? D'oh five. Do you root too? The ratio of mist ofhis nickel for the ratio of used to this right. Then our equaled five over it. We can actually substitute that in here we have. Hi. My mom comes Five squared. 25 Tim's route. You squared just to right with the quite a bit of recapture. Harassed went quite a bit if, um of their work, their souls just revealed that we found the area of the circle. And then we found the area of a triangle. Um, and just know that the killed my uncle. And then we track it and find the area of the shade reading. He pulled pie much worn out. Um, And then we found a radius using this. 45 45 90. This is the area of arcade region right here. And that's in unit of Children. Very good.

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