I have no idea how to go about this problem so any advice would be greatly appreciated.
If you show that the two smaller triangles, MRA and MBC, have the same area, then you're done, I think.
What can you say about the measures of angles RMA and BMC?
What can you say about the measures of angles MCB and MAR?
What then can you say about the third angles of each of the two smaller triangles?
What then can you say about these two triangles?
By definition of "midpoint", what can you say about the lengths of segments (that is, of sides) MR and MB?
What then can you conclude about the two smaller triangles?
Instead, try following the step-by-step instructions provided earlier:
Look at the second pair of angles listed. What can you conclude, using the fact that the top and bottom sides of the trapezoid are (what sort of) lines?
Once you have two pairs of congruent angles, what can you say about the third pair of angles?
What does this say about the two triangles?
Once you have those sorts of triangles, what does the congruency of one included side say?