Stuff :)

Look at the above image. If we split up the ellipse thingy into two and put them in the regions colored blue and red, then, we get the following image -

As you can see now, there is a right-isosceles triangle in the middle of the quarter-circle. It has a base and height of 44, so its area is 4×4×12=84 \times 4 \times \dfrac{1}{2} = 8.

The quarter-circle has an area of πr24=π424=4π\dfrac{\pi r^{2}}{4} = \dfrac{\pi 4^{2}}{4} = 4 \pi

A small GIF showing all the stuff I said above, if it was to hard to understand -

Thus, the orange area is

4π8\boxed{4 \pi - 8}


An alternative solution for those who think the above is felony (lol)

As proved in the preface, the area of the regions shaded blue in the above image have an area of 4π4 - \pi each.

Now, the remaining white regions are the regions shaded red in the image below. These have radii of length 22 each, so they're areas are π\pi each.

So, the total white area is π+π+4π+4π=8\pi + \pi + 4 - \pi + 4 - \pi = 8. Now, the orange area is equal to the area of the main quarter-circle minus the white regions area.

We have already calculated that the area of the main to be 4π4 \pi.

Thus, again the answer is 4π8\boxed{4\pi - 8}

Note by Percy Jackson
2 months, 2 weeks ago

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1 vote

  Easy Math Editor

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Comments

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@NSCS 747 - I just set up a rickroll comment for BM in the book choices daily challenge lol

Percy Jackson - 22 hours ago

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Well you have gone from spamming to rickrolling, I like the improvement, I await what’s next

Jason Gomez - 16 hours ago

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btw check his reply lmao!!!

Percy Jackson - 15 hours ago

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@Percy Jackson Btw I made a note just for private chat purposes check it out

Jason Gomez - 15 hours ago

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@Percy Jackson I saw, I realised something was wrong and then clicked,so wasn’t surprised

Jason Gomez - 15 hours ago

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@Jason Gomez lol

Percy Jackson - 11 hours ago

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not really, this one's special, coz nscs wanted to do it, but he didn't or i guess his rickroll failed, so I'm trying to rickroll BM, but no one else

Percy Jackson - 15 hours ago

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@Jason Gomez - Couldn't see your last comment, coz you deleted the comment thread by then. Any chance you could post it here?

Percy Jackson - 4 days, 13 hours ago

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I just said no worries because I deleted my comment, how do you not see it tho, u were in the comment thread, I always see this ghostly deleted comment threads I make, I assumed everyone else in the comment thread could also see it

Jason Gomez - 4 days, 13 hours ago

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Only you can see it as you deleted your comment. Others don't see anything. Its how people annoy others sometimes, give 'em a 100 notifs and then delete the comments :P

Percy Jackson - 4 days, 13 hours ago

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@Percy Jackson @Percy Jackson Lol, was planning to do the same suddenly, but let’s keep that for later

Jason Gomez - 4 days, 13 hours ago

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@Jason Gomez Haha, I won't fall for something that simple, it will have to be something big :)

Percy Jackson - 4 days, 12 hours ago

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@Percy Jackson Not for the challenge, just to annoy you, no one will ever fall for that

Jason Gomez - 4 days, 12 hours ago

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@Jason Gomez Ok, I am not going to reply if I see 4+ notifications from you lol :P

Percy Jackson - 4 days, 12 hours ago

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@Percy Jackson That would kinda promote me to do more :)

Jason Gomez - 4 days, 12 hours ago

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@Jason Gomez lmao I just opened brilliant and there were like 35 notifications so my first thought was you spammed me, until i realized i hadn't been here for a day, which is apparently enough time to get 30+ messages lol

Percy Jackson - 2 days, 15 hours ago

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@Percy Jackson Today I was out for six hours(sleeping) and was hit by 78 notifs (I am not popular as you are and get max 20 notifs per day) and I thought you did it, lol, Sarah Alam and Broekhuis were the culprits spamming so much in yesterday’s daily challenge

Jason Gomez - 1 day, 23 hours ago

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@Jason Gomez Not my fault that we were having an eleven person party without the people we were having a party for. Eleven people can do a lot of messages. Granted, it was me, S Broekhuis and his nine other split personalities. We were having a party for Julius/Confused. It’s deleted now, but we were talking about hypothetical situations where people had multiple split personalities and we started quoting 80s song lyrics. One of them was ‘Mr Blue Sky’ by the ELO Electric Light Orchestra. (Scientifically proven to be the worlds happiest song.) Then I had to go to bed and Broekhuis had to go walk his dog. And then the comments we were replying to got deleted. There was no evidence of our party. And then Jason Gomez began teaching me how to mention people. That was almost as long of a conversation.

Sarah Alam - 4 hours ago

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@Jason Gomez I'm not thaaaat popular, like a little bit I guess. Just got lucky, all the big solution makers were offline and my solutions scored at that time, that's all. I got 9 notifs today coz I didn't even see yesterday's challenge lol

Percy Jackson - 1 day, 15 hours ago

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@Percy Jackson Go check the “party” they were having with the “confused”

Jason Gomez - 1 day, 15 hours ago

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@Jason Gomez Wait what??? I don't see anything...

Percy Jackson - 1 day, 15 hours ago

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@Percy Jackson Yup it’s gone

Jason Gomez - 1 day, 15 hours ago

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@Jason Gomez Oh, k 👍

Percy Jackson - 1 day, 15 hours ago

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@Percy Jackson I leave for one day and this happens

Nico di Angelo - 1 day, 13 hours ago

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@Nico di Angelo haha lol sry nico

Percy Jackson - 22 hours ago

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@Percy Jackson So when are we going to the waystation?

Nico di Angelo - 12 hours ago

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@Nico di Angelo Around the end of june, so that way we can stay there and all of us can come back for the fireworks show on the beach for July 4th.

Percy Jackson - 11 hours ago

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@Percy Jackson I have been experimenting with the heapesutes campers, we have made a new kind of firework, that makes a miniature black void.

Nico di Angelo - 11 hours ago

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@Nico di Angelo Nice, i bet you'll love that one :P

Percy Jackson - 11 hours ago

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@Percy Jackson 53 notifications

Nico di Angelo - 1 day, 13 hours ago

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@Percy Jackson Adjacent pieces

Jason Gomez - 1 day, 15 hours ago

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@Jason Gomez Yes, I checked it there's no party of confused or anything? Mention me there!!!

Percy Jackson - 1 day, 15 hours ago

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@Percy Jackson Oh sry it’s day before yesterday

Jason Gomez - 1 day, 15 hours ago

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@Percy Jackson I was just looking up on your historical notes, and figured there is a lot to spam(actually more of a lot of genuine info to contribute), might attack on an unsuspecting day, you may start preparing those chubby fingers of yours, for a lot of notifs will need to be dismissed( read thru some, I think I might have somewhat of a lead in that impossible mathathon question).

Jason Gomez - 2 days, 15 hours ago

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@Jason Gomez lol i'll keep a lookout and also, the mathathon problem's been solved already :)

Percy Jackson - 1 day, 15 hours ago

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I've deleted most of my comments, kindly do the same peasants @Siddharth Chakravarty, @Frisk Dreemurr, @Krity Kamal, @Nikolas Кraj, @Nico di Angelo, @Will Solace

Percy Jackson - 1 week, 5 days ago

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dam, must have written weird stuff there

Nikolas Кraj - 1 week, 5 days ago

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Curious: Is "dam" a curse word? I have thought it was acceptable

Nikolas Кraj - 1 week, 4 days ago

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@Nikolas Кraj No, its a Percy Jackson reference. Like an inside joke only those that have read the books will understand.

Percy Jackson - 1 week, 3 days ago

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@Percy Jackson nice

Nikolas Кraj - 1 week, 3 days ago

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@Nikolas Кraj Ya well here's the gist of it -

A girl knows only old English not the more modern one so she speaks funny sometimes. Once, Percy, Zoe (the girl's name), Thalia and Grover (two other friends) go to Hoover Dam, and after deciding they should eat, Zoe says "Let us go to the dam snack bar". The other 3 start laughing saying 'I need a dam T-shirt' or 'I need to use the dam restroom' and laugh, and then Zoe is like 'what is funny? I do not understand' lmao

Percy Jackson - 1 week, 3 days ago

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@Percy Jackson Haha! Well, you could say that Zoe (a French name?) was 'damed' saying that.

Maybe it's time to upgrade her skills of English, cause a girl talking like in those medieval movies would sound like one in the lord of the rings.

I can imagine that guy from Clerks describing the trilogies:

" Here is the first movie. (walks funny)*"

" Here is the second movie. (Pretends to almost slip and walks funny)*"

" Are you ready for the third one ?(walks and imitates throwing a ring)*"

Nikolas Кraj - 1 week, 3 days ago

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@Nikolas Кraj lol no its a greek name for life, you know, coz the PJO series is about greek myths.

I haven't seen Clerks but I can totally see why he describes LotR that way lmao

Percy Jackson - 1 week, 3 days ago

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@Percy Jackson Huh, good to know. I could have met a girl named Zoe and said during a conversation: "Your name is lovely and rare, and it's French" and I'd not make it good (if she knew).

Nikolas Кraj - 1 week, 3 days ago

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@Nikolas Кraj lmao she'd be like 'vlacas', and you'd be like 'is that french for thank you?' lol (Dunno what vlacas is? Google it.)

Percy Jackson - 1 week, 2 days ago

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@Percy Jackson haha, (I know French btw). Well she would know Greek (and probably is a fan of ancient Greek history), so the date would be more like a history discussion (pretty great still). Worth spending time with her? Yes.

Nikolas Кraj - 1 week, 1 day ago

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@Nikolas Кraj Also, the Zoe from PJO would kill you for saying that. She's a hunter of artemis, she has sworn off men, and she has a lot of pointy silver arrows :)

Percy Jackson - 1 week ago

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@Percy Jackson well I ain't forcing anyone lol

Nikolas Кraj - 1 week ago

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@Nikolas Кraj lol you won't if you care for your life lmao

Percy Jackson - 6 days, 9 hours ago

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@Nikolas Кraj Ok we were discussing about dam and why its funny and whether Zoe is a greek or french name, not whether she'd be a great date...lmao

Percy Jackson - 1 week, 1 day ago

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@Percy Jackson I think zoe is french

Nico di Angelo - 1 week, 1 day ago

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@Nico di Angelo Nah, its a Greek name for 'life'. Like Zoe Nightshade, former Lieutenant of the Hunters of Artemis? Didn't know until i googled it tho lol

Percy Jackson - 1 week ago

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@Percy Jackson I never met her

Nico di Angelo - 1 week ago

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@Nico di Angelo The one who died on the quest to free artemis? The same one in which your sis died? The Titan's Curse quest, ya that one.

Percy Jackson - 1 week ago

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@Percy Jackson Don't speak of my sister

Nico di Angelo - 1 week ago

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@Nico di Angelo K, sorry...

Percy Jackson - 6 days, 9 hours ago

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@Percy Jackson It's fine, I talked to Jason yeaterday

Nico di Angelo - 6 days, 9 hours ago

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@Nico di Angelo He is lying he didn't talk to me at all

Jason Gomez - 5 days, 9 hours ago

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@Jason Gomez I'm talking about a dead demigod, named Jason grace

Nico di Angelo - 5 days, 7 hours ago

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@Nico di Angelo Yeah I know, you didn't talk to me, btw I already took a rebirth

Jason Gomez - 4 days, 23 hours ago

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@Jason Gomez STOP lol

Nikolas Кraj - 4 days, 5 hours ago

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@Nikolas Кraj Stop what???? Stop talking, stop dying, stop living, stop rebirthing, stop Apollo?, Stop Percy?, Stop You?????

Jason Gomez - 3 days, 21 hours ago

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@Jason Gomez flashbaks from 3rd grade teacher intensify*

Nikolas Кraj - 7 hours ago

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@Jason Gomez Stop percy

Nico di Angelo - 3 days, 9 hours ago

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@Nico di Angelo Ok shadow boy, what should I stop him from doing and what r my gains?

Jason Gomez - 3 days, 7 hours ago

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@Jason Gomez You can say that you have beat him

Nico di Angelo - 3 days, 5 hours ago

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@Nico di Angelo Everyone already knows I can so... it's just a waste of time and besides I don't fight good guys

Jason Gomez - 2 days, 20 hours ago

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@Jason Gomez bruh, i am like way better, i can totally beat you, i am the most powerful demigod!!!

Percy Jackson - 2 days, 15 hours ago

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@Percy Jackson I think Thalia fried your brain a little too much, previously I had a daily dosage of lightning bolts, but now I have gained the unlimited version, no use of controlling some H2H_2 and O2O_2,( yes that's the state of thy water after a through electrolysis)

Jason Gomez - 2 days, 15 hours ago

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@Jason Gomez Puh-lease, I can totally beat you, and even if I can't, I still will beat you (Plot armor suckas!)

Percy Jackson - 1 day, 15 hours ago

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@Percy Jackson Confirmed, Thalia struck you a little too hard, maybe another bolt will tighten those bolts, that reminds me I haven't met her since rebirth

Jason Gomez - 1 day, 15 hours ago

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@Jason Gomez you do that, I gtg, bye! (I know you mentioned me in yesterday's challenge and deleted it...)

Percy Jackson - 1 day, 15 hours ago

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@Percy Jackson Actually I didn't delete it

Jason Gomez - 1 day, 15 hours ago

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@Jason Gomez Then?

Percy Jackson - 1 day, 15 hours ago

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@Percy Jackson Moderator deleted mostly because there was too much spam there ( by Broekhuis and Sarah not me)

Jason Gomez - 1 day, 15 hours ago

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@Jason Gomez What were they talking about? I'm not sure Sarah would go on an off-topic convo in a dc, if a mod deleted it it has to be something terribly off-topic.

Percy Jackson - 1 day, 15 hours ago

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@Jason Gomez I thought you were mortal?

Nico di Angelo - 2 days, 12 hours ago

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@Jason Gomez Hi Jason! If you're in rebirth tho, how are you talking to us right now? I'm confused...?

Percy Jackson - 4 days, 15 hours ago

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@Percy Jackson I understand your confusion Percy, I can still talk to demigods and somehow I retain my memory slightly, gaining it back as time goes, don't know how but landed up as a fifteen year old with some Papadopolofoso..something guy who I was supposed to follow

Jason Gomez - 4 days, 13 hours ago

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@Jason Gomez You should know his name! If you're dead, then Burning Maze has already happened! That means you know who Lester is! You are forming a continuity error!!! lol

Percy Jackson - 4 days, 13 hours ago

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@Percy Jackson I am not dead.... I am talking to you bro, and as I mentioned I really lost my memory (real life too, long time since I read any of the Percy Jackson series)

Jason Gomez - 4 days, 12 hours ago

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@Jason Gomez Oh!? Ok...that's too much information...let me get Annabeth to help...bye! (gtg need breakfast!)

Percy Jackson - 4 days, 12 hours ago

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@Percy Jackson Lol, U should learn about schrodinger's cat on how to be alive and dead at the same time ( just realised I recently died acc to the story but three years before acc to reality )

Jason Gomez - 4 days, 12 hours ago

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@Jason Gomez What is going on? Jason? You were reborn as a 15 year old? I didn't know that was possible

Nico di Angelo - 4 days, 10 hours ago

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@Nico di Angelo Shadow boy needs to learn more about death and rebirth it seems, just kidding, I am a special case I think, I have a mission to do which I don't know yet, mostly another short life coming up

Jason Gomez - 4 days, 8 hours ago

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@Nico di Angelo Oh, he's not in rebirth? Ok, what did he say? Is he okay?

Percy Jackson - 5 days, 15 hours ago

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@Percy Jackson He says he is fine he is going to rebirth but he wanted to do something first, I don't know what. Btw this will be his second rebirth. My father told me so.

Nico di Angelo - 5 days, 11 hours ago

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@Nico di Angelo Ok

Percy Jackson - 4 days, 15 hours ago

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@Nikolas Кraj Ask seaweed brain, he'll laugh

Nico di Angelo - 1 week, 4 days ago

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@Nico di Angelo god of the seaweeds? :D

Nikolas Кraj - 1 week, 4 days ago

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@Nikolas Кraj No that's just what me and Annabeth call him, he only allows Annabeth to call him that though

Nico di Angelo - 1 week, 4 days ago

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@Nico di Angelo Stupid...

Percy Jackson - 1 week, 3 days ago

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True...these people are weird :P

(Also, its dam, not damn buddy, as Nico has already mentioned...we don't use that kind of language here)

Percy Jackson - 1 week, 5 days ago

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@Percy Jackson Thanks for the info!

Nikolas Кraj - 1 week, 4 days ago

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@Nikolas Кraj lol that was a Percy Jackson reference/inside joke

Percy Jackson - 1 week, 4 days ago

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Don't use that language, its "dam" if you don't understand as perc

Nico di Angelo - 1 week, 5 days ago

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@Nico di Angelo ah dam. I edited my comment btw

Nikolas Кraj - 1 week, 4 days ago

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@Nikolas Кraj Very

Nico di Angelo - 1 week, 4 days ago

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@Nikolas Кraj Good :)

Percy Jackson - 1 week, 4 days ago

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@Nico di Angelo Dam Neeks, stop calling me perc or I'll call you zombie prince (since hades is techinically like zombie king)

Percy Jackson - 1 week, 5 days ago

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@Percy Jackson Fine, i won't call you perc, how is seaweed brain?

Nico di Angelo - 1 week, 5 days ago

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@Nico di Angelo My name is Percy, so just call me that :)

Percy Jackson - 1 week, 4 days ago

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@Percy Jackson Then don't call Neeks

Nico di Angelo - 1 week, 4 days ago

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@Nico di Angelo Call me

Nico di Angelo - 1 week, 4 days ago

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@Nico di Angelo Ok Nico

Percy Jackson - 1 week, 3 days ago

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@Percy Jackson Thanks

Nico di Angelo - 1 week, 2 days ago

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@Nico di Angelo Your welcome :)

Percy Jackson - 1 week, 2 days ago

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@Percy Jackson Its cold, 34 degrees here, are you in New Rome?

Nico di Angelo - 1 week, 2 days ago

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@Nico di Angelo Yep, have to get through college...Anniebelle's not givin' me any breaks...too much for my brain...ugh...

Percy Jackson - 1 week, 2 days ago

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@Percy Jackson Fun, how is Annabeth? Oh, btw Juniper is pregnant, Grover is going to be a father

Nico di Angelo - 1 week, 2 days ago

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@Nico di Angelo Wait WHAT?!? That is so cool! Would it be a satyr or a nymph tho? I should leave the thinking to Annabeth. btw She's doing great, we've finally gotten over Jason's passing. Piper's taking it pretty well too. She came over for some downtime with Me, Annabeth, Frank and Hazel. Thinking of visiting Leo and Calypso at the Waystation soon. And that includes you too cuz, we're dragging you along :)

Percy Jackson - 1 week, 2 days ago

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@Percy Jackson I think it it will be a satyr, and no you aren't staging me along to see Leo, I despise him.

Nico di Angelo - 1 week, 2 days ago

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@Nico di Angelo K, I won't pull you along...but you know Annabeth will, and you can't escape her. Don't worry, Reyna and Thalia will be there.

Percy Jackson - 1 week, 1 day ago

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@Percy Jackson Reyna? She is ok

Nico di Angelo - 1 week, 1 day ago

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@Nico di Angelo Good, you're coming then :)

Percy Jackson - 1 week ago

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@Percy Jackson Maybe

Nico di Angelo - 1 week ago

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\hello \hello

NSCS 747 - 2 weeks, 4 days ago

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Damn, i get +30 notification /day from here

Nikolas Кraj - 3 weeks ago

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i have 40 rn

Nico di Angelo - 3 weeks ago

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i got 50 once, took me a few sec to clear notification

here is 41

Nikolas Кraj - 3 weeks ago

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@Nikolas Кraj when you click the 3 lines that show the number of notification, you can click "dismiss all" witch will clear 5 at a time.

Nico di Angelo - 3 weeks ago

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@Nico di Angelo ah thanks

Nikolas Кraj - 3 weeks ago

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@Nikolas Кraj yep

Nico di Angelo - 3 weeks ago

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The leaf is eq to the other orange thing fyi

Nikolas Кraj - 1 month, 2 weeks ago

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Wat?

Will Solace - 1 month, 2 weeks ago

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The orange leaf area = The other part that has orange color.

Nikolas Кraj - 1 month, 2 weeks ago

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@Nikolas Кraj Sorry about that, he gets confused about a lot of things.

Nico di Angelo - 1 month, 2 weeks ago

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Cool, what kind of music do you listen to?

Nico di Angelo - 2 months, 1 week ago

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I can end you

Nico di Angelo - 2 months, 1 week ago

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Hey

Nico di Angelo - 2 months, 2 weeks ago

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