B

Step 1: Area of a trapezoid = 12 × height × sum of the parallel sides[Formula.]

Step 2: From the figure, area of the trapezoid = 12 × DE × (AB + DC).

Step 3: 12 × h × ( AB + DC) = 36[Substitute the value of area of the trapezoid.]

Step 4: 12 × h × (6 + 3) = 36[Substitute AB = 6 ft, DC = 3 ft.]

Step 5: 12 × h × 9 = 36[Add 6 and 3 to get 9.]

Step 6: 9 × h = 72[Multiply both sides by 2.]

Step 7: h = 8 ft[Divide both sides by 9.]

Step 8: So, the height of the trapezoid ABCD is 8 ft.