Question

My question is attached,

thanks!

Answer 1

here,

Answer 2

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

Answer 3

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

Answer 4

its C

Answer 5

120pi + 36sqrt3

Answer 6

Thanks!

Answer 7

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

Answer 8

ty