To find the area of the quadrilateral, we need to find the area of the trapezoid and subtract the area of the right triangle at the bottom.
Area of trapezoid = (1/2) * (sum of parallel sides) * (height)
Area of trapezoid = (1/2) * (6 + 9) * 4
Area of trapezoid = 7.5 * 4
Area of trapezoid = 30 cm²
Area of right triangle = (1/2) * base * height
Area of right triangle = (1/2) * 6 * 4
Area of right triangle = 12 cm²
Area of quadrilateral = Area of trapezoid - Area of right triangle
Area of quadrilateral = 30 cm² - 12 cm²
Area of quadrilateral = 18 cm²
Therefore, the area of the quadrilateral is 18 cm².