find-the-area-of-the-shaded-region-diagram-cant-copy-5

Question

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

Kara Merfeld · Accepted Answer

Yes. This is a cool problem. I like one. Um, we have a circle, and we find the shaded region in it. But there&#x27;s a triangle. Tracked him from it. We&#x27;re told that this night here, it&#x27;s firing. Right. Um, we&#x27;re also I think this is implicitly this here, uh, screen, like to draw is the radius, um, of circle. It&#x27;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&#x27;s like it has been all doctor and then area of the triangle. It could be 1/2. I&#x27;m the base times height, 1/2 times the case times. He was a cool thing, though, Um, that&#x27;s that&#x27;s the center of circle. There. The point here on the basis of height or both. The radius. Um, where&#x27;s pretty red? So this is gonna be on 1/2. Uh, I&#x27;m the radius times the radius. That&#x27;s gonna be just the radius squared. But that&#x27;s assuming that they&#x27;re trying more and realistically. Sorry. That&#x27;s Syria&#x27;s one triangle. And there are two. Right, There&#x27;s the left, one in the right one So we can actually get rid of that 1/2. Well, it&#x27;s just kind of strike that out. Oh, great. Okay, so now the total area. Good day. Um oh, Sorry. Well, area that&#x27;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&#x27;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&#x27;ve got a 90 degree there. What? 90 degrees there? Andi, he&#x27;s reached 45 degrees. Um, so we&#x27;re we&#x27;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&#x27;s just one of things you have to have memorized from trigonometry. If you don&#x27;t have memorize to use appropriate, memorize it. It&#x27;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&#x27;ll be more explicit about it. So the ratio of whoa. Okay. Radius Who won nickel? D&#x27;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&#x27;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&#x27;s in unit of Children. Very good.

Kara Merfeld · Answer

Okay, So the simple strategy for finding the area of shaded regions that are, um, they have a whole and then we&#x27;ll say, is to just find just pretend that it&#x27;s a filled in circle and find the area of, like, this circle right, the whole thing, and then pretend there&#x27;s the hole in it. Later, just calculate the area of the whole and then just subtract that off. So let&#x27;s do that. We know that the area of a circle is equal to high times. The radius squared, right, squared for the big circle that is a radius of 24 meters, so that&#x27;s high times 24 squared meters. So the area of the big circle is 576 meters. Sorry, 507 6 py meters squared now have to find the area of a small circle, so we follow the same process. But let&#x27;s just jump off at this equation here, right? So we know we have area equals pi times the radius squared. However, this radius of the inner circle is only six meters, so this is area equals pie times six meters quantity squared work. It&#x27;s bad square. They were Elizabeth. Sure All right. Six squares. 36. So this is 36. Hi. Meter square. Okay, so now we just have to see practice to So we just have this, um 5 76 py meters squared, minus 36 year squared. Mom. So after we do that subtraction 5 76 minus 36 is 5 40 py meters squared. Um, and that&#x27;s the shade original. Right? So that&#x27;s just this part of it.

Georgiann Andersen · Answer

Okay? Never. 24 b of the square inside that square are four circles. We&#x27;re supposed to be touching each other, but I didn&#x27;t draw very well. You&#x27;re trying to find the area that is right here. Basically, in the middle of all, for those circles, we know that each side of the square is 20 inches. That means that if we draw from here from this side to this side, the diameter of each one of those circles is gonna be 10 inches. That means that the radius of each circle, if the diameter equals 10 inches, the radius is gonna equal five inches. We know that the area of a circle is equal to pi r squared so we can substitute in the so the area of one circle is going to equal the pie five square. You calculate that out, and that&#x27;s gonna be 25 pie, all four circles and for areas well equal four times the 25 pie which is gonna equal to 100 pie. You know, the area of ah square is going to be 2020 times 20 which is 400. So if we take the area of the square which is the 400. Subtract the area of the four circles, which is 100 pie. We&#x27;re gonna come up with 300 pie, which is approximately equal to 85.84 square feet.

Georgiann Andersen · Answer

Yeah. Huh? Hey, this is problem 26 and we have a circle inside of a circle, and we know that this is eight centimeters, and this section is also eats at centimeters. This is 180 degrees, and we&#x27;re trying to find we want to find the area of this shaded part here. So are large semi circle is gonna have a radius of eight plus eight for 16. This is centimeters. It&#x27;s our area of the large section at the large sector. Put it that way is going to be 100 and 80 over 360 times pi times the radius squared, which is 16 squared. And so that&#x27;s gonna end up equaling 1/2 pie times to 56 which is gonna equal to borrow two 12 centimeters squared. Yeah, the small sector. We&#x27;ll have an area of 180 over 360 times pi times eight square. It&#x27;s just gonna end up being when you calculate that out. It turns out to be 100 0.53 centimeter square. Now, because we want this the shaded section we&#x27;re gonna take the 402 0.12. We&#x27;re gonna subtract the 153 and we&#x27;re going to current come up with 301 0.59 centimeter square.

Georgiann Andersen · Answer

This is problem number 28. And what we have here is a circle inside that circle. We have this figure here similar to this. This side is can grill it with this side. This site is controlled with the other one. Center point is right here. This side is three inches. This side would also be three inches. This side is four inches and this side here will also be four inches. Okay, so we need to find the high part nous, which is gonna be the diameter of that circle. So we know that the high pot news squared is gonna be the same as three squared plus four squared. So that&#x27;s gonna be a nine plus 16. Which is it equals 25. That being said, we know that H equals five. It&#x27;s our diameter is five. So diameter equals five and our radius will be equal to 2.5. And the&#x27;s Aaron meters, not inches. I apologize. Sell a radius is 2.5 meters. Now to find the area we know the area is pi r squared so we can make this pie and 2.5 squared. This is actually that going to be 19.6 to 5 meters square now the area of a triangle. We know it&#x27;s 1/2 based times the height. So in this case, be it night. We know it&#x27;s gonna be 1/2 times, three times four, which is going to be six meters square, but we have two of those. So to solve all this, we&#x27;re gonna take the area of the circle, which is 19.6 to 5, and we&#x27;re gonna subtract out two times the area of a triangle. So we&#x27;re gonna have 19.6 to 5. It&#x27;s a track 12. We&#x27;re gonna end up with 7.6 to 5 meters squared for the sheer shaded area.

Melissa Salvador · Answer

Okay, so here we have a rectangle and we want to find area. So the area of your rectangle is base times height. So this would be I two and want their feet time, six feet so that a calculator and we get to the area would be 14 feet squared.

Problem

Find the area of the shaded region. (Diagram Can…

Problem 27 Hard Difficulty

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

Answer

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

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

Geometry A Common Core Curriculum

Megan C.

Maria G.

Samuel H.

Michael D.

(A few) Circle Theorems

Angles and Cirlce Theorems with chords and tangents

Ron Larson, Laurie BoswellGeometry A Common Core Curriculum

Megan C.

Maria G.

Samuel H.

Michael D.

Ron Larson, Laurie Boswell

Geometry A Common Core Curriculum