# 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 $4$, so its area is $4 \times 4 \times \dfrac{1}{2} = 8$.

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

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

Thus, the orange area is

$\boxed{4 \pi - 8}$

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 $4 - \pi$ each.

Now, the remaining white regions are the regions shaded red in the image below. These have radii of length $2$ each, so they're areas are $\pi$ each.

So, the total white area is $\pi + \pi + 4 - \pi + 4 - \pi = 8$. 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 $4 \pi$.

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

Note by Percy Jackson
2 months, 2 weeks ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

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Sort by:

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

- 22 hours ago

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

- 16 hours ago

- 15 hours ago

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

- 15 hours ago

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

- 15 hours ago

lol

- 11 hours ago

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

- 15 hours ago

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

- 4 days, 13 hours ago

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

- 4 days, 13 hours ago

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

- 4 days, 13 hours ago

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

- 4 days, 13 hours ago

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

- 4 days, 12 hours ago

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

- 4 days, 12 hours ago

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

- 4 days, 12 hours ago

That would kinda promote me to do more :)

- 4 days, 12 hours ago

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

- 2 days, 15 hours ago

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

- 1 day, 23 hours ago

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.

- 4 hours ago

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

- 1 day, 15 hours ago

Go check the “party” they were having with the “confused”

- 1 day, 15 hours ago

Wait what??? I don't see anything...

- 1 day, 15 hours ago

Yup it’s gone

- 1 day, 15 hours ago

Oh, k 👍

- 1 day, 15 hours ago

I leave for one day and this happens

- 1 day, 13 hours ago

haha lol sry nico

- 22 hours ago

So when are we going to the waystation?

- 12 hours ago

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.

- 11 hours ago

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

- 11 hours ago

Nice, i bet you'll love that one :P

- 11 hours ago

- 1 day, 13 hours ago

- 1 day, 15 hours ago

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

- 1 day, 15 hours ago

Oh sry it’s day before yesterday

- 1 day, 15 hours ago

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).

- 2 days, 15 hours ago

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

- 1 day, 15 hours ago

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

- 1 week, 5 days ago

dam, must have written weird stuff there

- 1 week, 5 days ago

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

- 1 week, 4 days ago

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

- 1 week, 3 days ago

nice

- 1 week, 3 days ago

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

- 1 week, 3 days ago

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)*"

- 1 week, 3 days ago

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

- 1 week, 3 days ago

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).

- 1 week, 3 days ago

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

- 1 week, 2 days ago

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.

- 1 week, 1 day ago

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 :)

- 1 week ago

well I ain't forcing anyone lol

- 1 week ago

lol you won't if you care for your life lmao

- 6 days, 9 hours ago

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

- 1 week, 1 day ago

I think zoe is french

- 1 week, 1 day ago

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

- 1 week ago

I never met her

- 1 week ago

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.

- 1 week ago

Don't speak of my sister

- 1 week ago

K, sorry...

- 6 days, 9 hours ago

It's fine, I talked to Jason yeaterday

- 6 days, 9 hours ago

He is lying he didn't talk to me at all

- 5 days, 9 hours ago

- 5 days, 7 hours ago

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

- 4 days, 23 hours ago

STOP lol

- 4 days, 5 hours ago

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

- 3 days, 21 hours ago

flashbaks from 3rd grade teacher intensify*

- 7 hours ago

Stop percy

- 3 days, 9 hours ago

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

- 3 days, 7 hours ago

You can say that you have beat him

- 3 days, 5 hours ago

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

- 2 days, 20 hours ago

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

- 2 days, 15 hours ago

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 $H_2$ and $O_2$,( yes that's the state of thy water after a through electrolysis)

- 2 days, 15 hours ago

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

- 1 day, 15 hours ago

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

- 1 day, 15 hours ago

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

- 1 day, 15 hours ago

Actually I didn't delete it

- 1 day, 15 hours ago

Then?

- 1 day, 15 hours ago

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

- 1 day, 15 hours ago

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.

- 1 day, 15 hours ago

I thought you were mortal?

- 2 days, 12 hours ago

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

- 4 days, 15 hours ago

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

- 4 days, 13 hours ago

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

- 4 days, 13 hours ago

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)

- 4 days, 12 hours ago

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

- 4 days, 12 hours ago

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 )

- 4 days, 12 hours ago

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

- 4 days, 10 hours ago

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

- 4 days, 8 hours ago

Oh, he's not in rebirth? Ok, what did he say? Is he okay?

- 5 days, 15 hours ago

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.

- 5 days, 11 hours ago

Ok

- 4 days, 15 hours ago

- 1 week, 4 days ago

god of the seaweeds? :D

- 1 week, 4 days ago

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

- 1 week, 4 days ago

Stupid...

- 1 week, 3 days ago

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)

- 1 week, 5 days ago

Thanks for the info!

- 1 week, 4 days ago

lol that was a Percy Jackson reference/inside joke

- 1 week, 4 days ago

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

- 1 week, 5 days ago

ah dam. I edited my comment btw

- 1 week, 4 days ago

Very

- 1 week, 4 days ago

Good :)

- 1 week, 4 days ago

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

- 1 week, 5 days ago

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

- 1 week, 5 days ago

My name is Percy, so just call me that :)

- 1 week, 4 days ago

Then don't call Neeks

- 1 week, 4 days ago

Call me

- 1 week, 4 days ago

Ok Nico

- 1 week, 3 days ago

Thanks

- 1 week, 2 days ago

- 1 week, 2 days ago

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

- 1 week, 2 days ago

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

- 1 week, 2 days ago

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

- 1 week, 2 days ago

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 :)

- 1 week, 2 days ago

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

- 1 week, 2 days ago

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.

- 1 week, 1 day ago

Reyna? She is ok

- 1 week, 1 day ago

Good, you're coming then :)

- 1 week ago

Maybe

- 1 week ago

$\hello$

- 2 weeks, 4 days ago

Damn, i get +30 notification /day from here

- 3 weeks ago

i have 40 rn

- 3 weeks ago

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

here is 41

- 3 weeks ago

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

- 3 weeks ago

ah thanks

- 3 weeks ago

yep

- 3 weeks ago

The leaf is eq to the other orange thing fyi

- 1 month, 2 weeks ago

Wat?

- 1 month, 2 weeks ago

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

- 1 month, 2 weeks ago

- 1 month, 2 weeks ago

Cool, what kind of music do you listen to?

- 2 months, 1 week ago

I can end you

- 2 months, 1 week ago

Hey

- 2 months, 2 weeks ago