The length of an arc of a circle is just a portion of the circumference of a circle.  Given that the circumference of a circle is 2  r, a portion of that is just a fraction of (x many degrees / 360 degrees) 2  r.
    The area of a circle is  r.  A portion of that is the area of a sector.  Thus (x many degrees / 360 degrees) times  r = the area of a sector.
 
 

(1) If an arc is 32 degrees long and has a radius of 5 meters, how long is it?

(2) How many arcs of 60 degrees will create a circle?

(3) If a sector has a radius of 2.3 meters and covers 3 radians, what is it's area?