Explanation:
a sector of a circle is like a piece of pie or pizza. a kind of triangle, but with the baseline not being a straight line but a round piece (arc) of the circle circumference.
it represents a piece of the whole circle. its area and the length of the arc a "baseline" have the same ratio to the full circle's area and circumference, as the given angle of the sector has with the full circle's 360°.
so, the sector ratio is
66/360 = 33/180 = 0.183333333...
the area of a circle is
pi×r²
with r being the radius.
the area of our sector is therefore
pi×8² × 33/180 = pi×64 × 33/180 =
= 36.8613538... cm²
the circumference (the full arc) around the whole circle is
2×pi×r
again, r is the radius.
the arc length of our sector is
2×pi×8 × 33/180 = 9.215338451... cm
the perimeter of our sector is now that arc length plus two times the radius (the "legs" of the "round triangle") :
9.215338451... + 2×8 = 25.21533845... cm