Yes I'm dumb but how the fuck do you find the area of this shaded region

Yes I'm dumb but how the fuck do you find the area of this shaded region

Saw it online and am stumped

Other urls found in this thread:

dummies.com/education/math/geometry/how-to-determine-the-area-of-sectors-and-segments-of-a-circle/
twitter.com/NSFWRedditGif

first find the area of the circle. then determine the area of the grey area, then subtract.

A=πr2=π·62≈113.09734

i did that but i have no idea how to find shaded region since i can't find theta ? :(((((

ok so do you know how to find the area of a regular triangle?

you have two sides bro, use an inverse trig function to get the angle

divide it into a triangle and a sector like this
then use trig

ohh i see

then use law of cosines to find theta?

that makes sense thanks boy im a dumb faggot

Give me a minute

Gif not related

you could but thats going to make it harder(more steps because you just created another slice and still need to find the arc segment.

try dummies.com/education/math/geometry/how-to-determine-the-area-of-sectors-and-segments-of-a-circle/

but you can use law of cosines to find the inscribed angle and the area of the triangle.

...

I got 70.43

Just read more work from Euclid. Like Euclid's Elements

Engineer here. Shaded area is about 48.17 square cocks.

I'm an engineer

I literally would have had look up all the equations relating to trig and circles, even then I probably would have had to just look up the solution

You get better at math by practicing, don't ever look down on yourself for trying to learn, OP

Obviously wrong because you can easily work out the area should be close to 36 with brainlet geometry.

Dude, just guess.
It's like 18-25 squaresomething

Have I made any mistakes so far, Veeky Forums?

Like dis

Strange, I got:

[math]\frac{8\sqrt{5}}{9}(8 + 5\pi)[/math]

Which is aprox 47.12.

Going to assume the trig functions is causing the slight difference and my solution is correct.

The only one with a correct answer...

>Area larger than the area of the circle
Nah...

draw a line from the center to the top point. now it's super easy, find the angles and calculate

use Pythagorean theorem, the area of a triangle, basic trig, and the area of a circle

Calculate the angle then integrate

I got [math]18(\pi-2\sin^{-1}\frac{2}{3}+\frac{4\sqrt{5}}{9})[/math]

It's not a right triangle idiot
Its easiest to find the white area, using the area of half a circle and above the chord. The subtraction from full circle.

how do you find the area above the chord?

The area of the circle is 36 pi.
Taking away the lower half gives 18 pi.
Bisect the chord though the center of the circle to get a right triangles with sides 4 and 6.
Calculate the unknown side using Pythagorus' theorem.
With all three sides and one angle known, use Law of Cosines to find all angles.
Double the central angle to find the central angle of the whole sector defined by the chord.
Calculate the area of the whole sector.
Subtract double the area of the right triangle to find the area of the circle segment cut off by the chord.
Subtract that amount from 18 pi.
Done.

I have no idea how to calculate this shit, but my first instinkt to was to so something like this.

Rotating the top part to a different part of the circle should't change the area right? still have the exact same cut of the circle with both white parts.

Not sure if it makes it any easier though.

My god you people are stupid. Just find the area of the chord and subtract it from half the area of the circle.

Chords don't have areas, dumbass. Did you mean the circle segment cut off by the chord? Of course you did. That has an area.

he obviously meant that, you gigantic fucking autist

you're a smart one. did you finish top of your class?

Just solved it with a double integral.
Its 47 something

There is no shading, so A=0.

36pi is about 113. That area isn't even half the area of the circle, so where are all these brainlet answers with absurdly high numbers coming from?

It's this. Also the picture is drawn stupid.