One angle of a rhombus is 120 degrees. The perimeter
is 96m.  Find the Area.

A rhombus is a parallelogram with all four sides equal:        
 

      _____________
     /            /
    /            /
   /            /    
  /            /
 /            /
 ¯¯¯¯¯¯¯¯¯¯¯¯¯

The formula for the area of any parallogram is bh
So we draw in the height, h. The perimeter is 96,
and since a rhombus has four equal sides, each side
is 1/4 of 96m, or 24m.  Also since the measure
of the obtuse interior angle on the lower right
corner is 120°, the acute angle on the lower left
corner must be supplementary to it, or 180°-120°
which is 60°: 

      _____________
     /|   24m     /
    / |          /
24m/  |h        / 24m
  /   |        /
 /60° |   120°/
 ¯¯¯¯¯¯¯¯¯¯¯¯¯

Now from the right triangle on the left of the
rhombus, 

             h
sin(60°) = ----
            24

Multiply both sides by 24:

24·sin(60°) = h
       _ 
   24(Ö3/2) = h

Simplify:
          _
       12Ö3 = h

The formula for the area is

          A = base×height

The base is the bottom side which is 24m
                            _
The height is h which is 12Ö3
                      _
So        A = (24)(12Ö3)
                  _
          A = 288Ö3 or approximately 498.83063276

I'd round that off to 499m², or however your
teacher tells you.

Edwin