Mathematics
OpenStudy (anonymous):

My question is attached, thanks!

OpenStudy (anonymous):

here,

OpenStudy (anonymous):

the area of segment = area of sector - area triangle = 1/6 * pi * 12^2 - (1/2)*12^2 sin 60 shaded area = pi * 12^2 - area segment = 452.39 - (75.4 - 62.35) = 452.39 - 13.05 = 439.34

OpenStudy (anonymous):

oh - they wanted it in surd form - ill have to check that out

OpenStudy (anonymous):

its C

OpenStudy (anonymous):

120pi + 36sqrt3

OpenStudy (anonymous):

Thanks!

OpenStudy (anonymous):

the area of the shaded part is the area of the whole circle minus that little sliver. or we could say it is the area of the circle - area of that sector + the area of that triangle. lets remember a few formulas: area of a circle : pi r^2 area of a sector: 1/2 (angle) (radius)^2 area of an equilateral triangle:( side^2 * sqrt(3))/4, and in this case the side of the triangle is the radius. so now we have: $\pi r^2 - 1/2(\theta r^2)+(r^2\sqrt{3})/4$ then some algebra

OpenStudy (anonymous):

ty