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 $\boxed{4\pi - 8}$

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
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`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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

Percy Jackson - 1 month, 2 weeks ago

Hey

Nico di Angelo - 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

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

@Nico di Angelo – lol ok Death Breath :P

@Percy Jackson – Ok Seaweed Brain

@Nico di Angelo – 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...

@Percy Jackson – 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"?

@Nico di Angelo – 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

@Percy Jackson – Do you think Grover or Tyson could help? they are good at finding monsters

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

@Percy Jackson – Will doesn't want me to use my powers anymore so, yeah

@Nico di Angelo – Well, you have to obey 'Doctor's orders', don't you :P

@Percy Jackson – Yeah, I guess

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

@Percy Jackson – 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

@Nico di Angelo – I am the best alive swordsman in the last 300 years, second only to Luke!!

I can end you

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!

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

@Nico di Angelo – I can control your blood, your movements, your brain...basically, I can own you :)

@Percy Jackson – you promised Annabeth not to do that

@Nico di Angelo – 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...

@Percy Jackson – I breath darkness and shadow, you have nothing on me

@Nico di Angelo – Ya, ya, keep talking neeks, you know i'm better...

@Percy Jackson – yeah, you might have me beat in stupidity.

@Nico di Angelo – 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)

@Percy Jackson – speaking of the Argo II, how is coach hedge?

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

Percy Jackson - 1 month, 1 week ago

@Nico di Angelo – You obliterated his what!?!

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

Frisk Dreemurr - 1 month, 1 week ago

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

@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...

Notification link - link

you cant

Nico di Angelo - 1 month, 1 week ago

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

Siddharth Chakravarty - 1 month, 1 week ago

:( can't...lol

Hi Percy, here is Mahdi Raza's reply:

Brilliant Mathematics Staff - 1 month, 1 week ago

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

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

Krity Kamal - 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.

Krity Kamal - 2 days ago

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

Brilliant Mathematics Staff - 1 day, 3 hours ago

@Brilliant Mathematics – 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!

Krity Kamal - 4 hours ago

Cool, what kind of music do you listen to?

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

Fall ou boy is pretty good.

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

@Nico di Angelo – ...

@Percy Jackson – What?

@Nico di Angelo – nothing :)

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

@Nico di Angelo – We love the Earth, it is our planet :)

@Percy Jackson – We love the Earth, it is our home :(

@Percy Jackson – We are gonna die if we don’t reduce emissions

NSCS 747 - 1 month ago

@Nscs 747 – We are all gonna die anyway.

Nico di Angelo - 1 month ago

@Nscs 747 – lmao lol

Percy Jackson - 1 month ago

@Percy Jackson – what is so funny?

@Nico di Angelo – nothing...i just like laughing..and blue...and water...and..Gah stupid ADHD

@Percy Jackson – How was your new years, perc?

Nico di Angelo - 2 weeks, 6 days ago

@Nico di Angelo – good. i am waiting for the 4th of july. fireworks on the beach :)

Percy Jackson - 2 weeks, 6 days ago

@Percy Jackson – Yeah, i wonder what the hephaestus kids will cook up.

@Nico di Angelo – yup, leo always has the wackiest, but coolest ideas lol

@Percy Jackson – wait, leos going to be there?

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

Percy Jackson - 2 weeks, 5 days ago

@Percy Jackson – calypso is a anchovy brand i use

NSCS 747 - 2 weeks, 5 days ago

@Nscs 747 – Calypso is Leo valdez's girlfriend. She is the daughter of the titan atlas. SHe's from Greek Mytho

@Percy Jackson – bruh its the beggining of the year and you are already thinking about july

@Nscs 747 – not really. in the series, the camp have a fireworks show at the beach every 4th of july. there aren't many other celebrations.

@Percy Jackson – new years birthdays god day or something

@Nscs 747 – 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.

@Percy Jackson – Brilliant is kinda boring for me now no good dramas to watch on here

@Nscs 747 – lol yeah same

The leaf is eq to the other orange thing fyi

Nikolas Кraj - 3 weeks ago

Wat?

Will Solace - 2 weeks, 6 days ago

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

Nikolas Кraj - 2 weeks, 6 days ago

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

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$