# 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
1 month, 2 weeks ago

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Sort by:

I just created this to save the code of my solution someplace, seeing as I was encountering a bug in my solution today :)

- 1 month, 2 weeks ago

Hey

- 1 month, 2 weeks ago

89? Seriosuly Neeks? I know you were born in the old ages, but you're still a teen kiddo :P

- 1 month, 2 weeks ago

Yeah I'm actually older than that but it wouldn't let me put that in 96

- 1 month, 2 weeks ago

lol ok Death Breath :P

- 1 month, 2 weeks ago

Ok Seaweed Brain

- 1 month, 2 weeks ago

Hey, only Annabeth gets to call me that!!! btw What happened in Albania that you and Reyna wouldn't talk about? Reyna got her dogs to chase me around camp when i asked her, so...

- 1 month, 2 weeks ago

Nothing

Perhaps we should stop fighting, you know what happened the last time the children of the big three fought. Do you happen to know what monster is causing this "Virus"?

- 1 month, 2 weeks ago

Ok...I'm guessing there's some really tiny, annoying monster going around in people and killing them...dunno, leave the thinking to the Athena kids, we just gotta kick monster ass lol

- 1 month, 2 weeks ago

Do you think Grover or Tyson could help? they are good at finding monsters

- 1 month, 2 weeks ago

Maybe, but let's leave it to the others to find them...I need a break from battles, quests and trying not to die...

- 1 month, 2 weeks ago

Will doesn't want me to use my powers anymore so, yeah

- 1 month, 2 weeks ago

Well, you have to obey 'Doctor's orders', don't you :P

- 1 month, 2 weeks ago

Yeah, I guess

- 1 month, 2 weeks ago

K...wait, why did ya add 'Arguing with Percy' to your interests!?!?! Me. you. at. the. arena. right. now.

- 1 month, 2 weeks ago

You got to talk to Will about that, and I put that because we have good arguments.

Also I don't want to kick your ass, not in the mood

- 1 month, 2 weeks ago

I am the best alive swordsman in the last 300 years, second only to Luke!!

- 1 month, 2 weeks ago

I can end you

- 1 month, 2 weeks ago

Nah, you said it yourself that I am the most powerful demigod you've ever seen, so unless you never looked in a mirror (which I'm sure you did), I can whoop yo ass!

- 1 month, 2 weeks ago

Do you know what I did to Bryce? I literally obliterated his soal and sent him to hell

- 1 month, 2 weeks ago

- 1 month, 2 weeks ago

you promised Annabeth not to do that

- 1 month, 2 weeks ago

Poison...not blood...and I can control water vapor, so I can remove the air from your lungs, or make all the water freeze on you to encase you in ice, etc...

- 1 month, 2 weeks ago

I breath darkness and shadow, you have nothing on me

- 1 month, 2 weeks ago

Ya, ya, keep talking neeks, you know i'm better...

- 1 month, 2 weeks ago

yeah, you might have me beat in stupidity.

- 1 month, 2 weeks ago

Sure, whatever floats your boat death breath...(actually, your boat won't float, coz my dad won't allow it, and neither will I uhless its the Argo II, so bummer for you :P)

- 1 month, 2 weeks ago

speaking of the Argo II, how is coach hedge?

- 1 month, 2 weeks ago

shudder can't get anywhere near him and Chuck...baseball bats are my new fear...they're fine tho, a happy family...

- 1 month, 1 week ago

What's his cloud nymph wife's name?

- 1 month, 1 week ago

Mellie I think

- 1 month, 1 week ago

Ah, ok

- 1 month, 1 week ago

You obliterated his what!?!

You obliterated his..... dirty pond? And you speak of this as a high achievement. How pathetic... lol

- 1 month, 1 week ago

English is funny...It takes revenge when you make spelling mistakes...coz those spelling mistakes turn into unexpected things...

- 1 month, 1 week ago

@Brilliant Mathematics - How do we reply if someone sends us a reply in a Daily Problem that has expired? Mahdi Raza recently sent me a reply, but I can't see what it is because the problem 'Triangles in a Triangle' has expired...

- 1 month, 1 week ago

you cant

- 1 month, 1 week ago

Didn't ask you Death boy :)

- 1 month, 1 week ago

Karpos

- 1 month, 1 week ago

Who or what is that exactly?

- 1 month, 1 week ago

well, today it is a ski jacket brand, but in ancient Greek, it means bitch

- 1 month, 1 week ago

...whatever neeks...stop cursing...

- 1 month, 1 week ago

yes'm

- 1 month, 1 week ago

Good...

- 1 month, 1 week ago

Take premium, we premium users can see the expired challenges as they are in archives just for us.

- 1 month, 1 week ago

:( can't...lol

- 1 month, 1 week ago

same, too costly

- 1 month, 1 week ago

Hi Percy, here is Mahdi Raza's reply:

Staff - 1 month, 1 week ago

Thanks! (there was a lot of wisdom there lol)

- 1 month, 1 week ago

@Percy Jackson,Sorry for using your page. I was not able to mention brilliant mathematics any where else.

- 1 day, 23 hours ago

@Brilliant Mathematics,I am not able to comment and post solutions from late 2 months from my original id.Please resolve this problem.

- 2 days ago

The other account was suspected of vote manipulation and has its abilities revoked. We do not support users using multiple accounts on Brilliant.

Staff - 1 day, 3 hours ago

I made another account after you people have disabled me from commenting and posting solutions. Plus i am still able to upvote solutions from that account(lol). So,what's the point of disabling me???? Heck!

- 4 hours ago

because they wanted to

- 4 hours ago

Lol. I think i should delete that account.

- 4 hours ago

maybe, they are soo strict on here, they deleted my riddles. i haven't seen perc in a while, do you think he is ok?

- 4 hours ago

You created a bunch of accounts to upvote your own solution.

Staff - 3 hours ago

what a cheater, hey could you undelete my riddles?

- 3 hours ago

We do not want to feature riddles on this site.

Staff - 2 hours ago

oh, ok, that sucks, i think Elija has some tho

- 2 hours ago

Fine. @Brilliant Mathematics

- 41 minutes ago

yeah, get deleted

- 38 minutes ago

Cool, what kind of music do you listen to?

- 1 month, 1 week ago

CHVRCHES, Marshmello, Alan Walker, Bars & Melody, Fall Out Boy are a few of my fav artist. I like Megalovania by Toby Fox too :)

- 1 month, 1 week ago

Fall ou boy is pretty good.

I'm more into Eminem I like the death aspect to it

- 1 month, 1 week ago

...

- 1 month, 1 week ago

What?

- 1 month, 1 week ago

nothing :)

- 1 month, 1 week ago

Hey, it's good music. I'm kinda in to a few songs by lil Dicky

- 1 month, 1 week ago

We love the Earth, it is our planet :)

- 1 month, 1 week ago

We love the Earth, it is our home :(

- 1 month, 1 week ago

We are gonna die if we don’t reduce emissions

- 1 month ago

We are all gonna die anyway.

- 1 month ago

sucker...

- 1 month ago

lmao lol

- 1 month ago

what is so funny?

- 1 month ago

nothing...i just like laughing..and blue...and water...and..Gah stupid ADHD

- 1 month ago

How was your new years, perc?

- 2 weeks, 6 days ago

good. i am waiting for the 4th of july. fireworks on the beach :)

- 2 weeks, 6 days ago

Yeah, i wonder what the hephaestus kids will cook up.

- 2 weeks, 6 days ago

yup, leo always has the wackiest, but coolest ideas lol

- 2 weeks, 6 days ago

wait, leos going to be there?

- 2 weeks, 6 days ago

Yeah he is visiting with Calypso. They're leaving the waystation and coming to camp for a few days.

- 2 weeks, 5 days ago

calypso is a anchovy brand i use

- 2 weeks, 5 days ago

Calypso is Leo valdez's girlfriend. She is the daughter of the titan atlas. SHe's from Greek Mytho

- 2 weeks, 5 days ago

bruh its the beggining of the year and you are already thinking about july

- 2 weeks, 5 days ago

not really. in the series, the camp have a fireworks show at the beach every 4th of july. there aren't many other celebrations.

- 2 weeks, 5 days ago

new years birthdays god day or something

- 2 weeks, 5 days ago

Nope, we celebrate after winning wars and on July 4th. For birthdays and stuff we only have tiny parties. The whole camp parties on the 4th.

- 2 weeks, 5 days ago

Brilliant is kinda boring for me now no good dramas to watch on here

- 2 weeks, 5 days ago

lol yeah same

- 2 weeks, 5 days ago

The leaf is eq to the other orange thing fyi

- 3 weeks ago

Wat?

- 2 weeks, 6 days ago

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

- 2 weeks, 6 days ago