In the figure below, $O$ is the center of the circle, and the radius of the circle is $8$. Angle $\angle BOA$ is right. What is the area of the filled-in (purple) region? Give your answer in exact form (which may involve pi). In other words, don't round off (but do simplify if you can).
Need to see the PURPLE area ...is it in the 90 degree area ...or the 270 degree area ...or other?
\([asy] size(4cm); pair o=(0,0); pair a=(-sqrt(2)/2,-sqrt(2)/2); pair b=(sqrt(2)/2,-sqrt(2)/2); path p=Arc(o,1,225,315)--b--a--cycle; fill(p,purple); dot(o); dot(a); dot(b); draw(o--b--a--o); draw(a/8--(a+b)/8--b/8); draw(Circle(o,1)); label("$O$",o,N); label("$A$",a,SW); label("$B$",b,SE); [/asy]\).
This is a mess, I'm adding onto this mess
I remember this one from the other day.....it just wants the area between sector BOA and triangle BOA
Area of sector = pi * 8^2 * (90/360) = 16 pi
Area of triangle BOA = (1/2) (8)^2 = 32
Purple area = 16 pi -32 = 16 ( pi - 2)