Area Of A Parallelogram

To solve the problem, we need to find the areas of the parallelogram and the quadrilateral , then compare their ratios.

1. Begin by identifying vectors. From the question: , , and .
2. The area of parallelogram with sides and is given by the magnitude of the cross product: .
3. For quadrilateral , split it into two triangles: and .
   1. Area of . . Therefore: . So, the area of .
   2. Area of . Calculate , because . Thus, the area of .
4. So, the area of quadrilateral is the sum of the areas of the two triangles: .
5. Finally, the ratio of the area of quadrilateral to parallelogram is: .

Thus, the correct answer is 8.