The area of a trapezoid can be found using the formula:
Area = 1/2 * (sum of the lengths of the parallel sides) * height
In this case, the sum of the lengths of the parallel sides is 6 + 10 = 16 centimeters, and the height is 6 centimeters.
Therefore, the area of the quadrilateral is:
Area = 1/2 * 16 * 6
Area = 8 * 6
Area = 48 square centimeters
So, the area of the quadrilateral is 48 square centimeters.