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

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.