The area of the quadrilateral can be calculated using the formula for the area of a trapezoid, which is (1/2) * (sum of the lengths of the parallel sides) * (height).
Since the perpendicular line divides the parallelogram into two trapezoids, we can calculate the area of each trapezoid separately and then add them together.
For the first trapezoid:
- Top side = 7 cm
- Bottom side = 12 cm
- Height = 12 cm
- Area = (1/2) * (7 + 12) * 12 = (1/2) * 19 * 12 = 114 cm^2
For the second trapezoid:
- Top side = 7 cm
- Bottom side = 12 cm
- Height = 7 cm
- Area = (1/2) * (7 + 12) * 7 = (1/2) * 19 * 7 = 66.5 cm^2
Therefore, the total area of the quadrilateral is 114 cm^2 + 66.5 cm^2 = 180.5 cm^2.