1) The angle bisector divides makes the segments on one side proportional to the corresponding segments on the other side.
3/4 = x/7.5
x = (3/4)*7.5 = 5.625
2) There are a number of ways to compute the area of the figure. I choose to divide it into a rectangle 8 units wide by 6 units high and two triangles. One triangle is 3 units wide and 2 high, the other is 6 units wide and 1 high. Then the total area is
(8*6)+(1/2)*(3*2 +6*1)
= 48 +6
= 54 units²