Just need help solving this problem.

19 sq. m
The easiest way is to split the shape into two rectangles and solve from there.
The first rectangle to spilt is the 5x3 and then solve:
A = lw = 3 x 5 = 15
The second rectangle is 4x1 because we must take out the section (3) used by the other rectangle:
A = lw = 1 x 4 = 4
Then add the areas together: