Explanation:
the radius of the circle is 10 in.
so, what is the area of the whole circle (which represents an angle of 360°) ?
the area of the circle is
pi×r² = pi×10² = 100pi
ok, now we don't need the area of the full 360°. we only need the area of 120°.
what would be the area of only 1° ?
I think that is fully clear : it would be the area of the full circle divided by 360 :
100pi / 360
and now, based on this, what is then the area of 120° ?
well, 120 times the area of 1° :
(100pi / 360) × 120 = 100pi × 120/360 = 100pi × 1/3 =
= 100pi/3 = 104.7197551... in² ≈
≈ 104.72 in²
so, you see, the area of a sector is always the area of the full circle multiplied by (angle/360).
the sector is nothing else than a fraction of the full circle.