Three ways to solve this problem: 1. Careful observation of the coordinates reveals that the side PQ is horizontal along the line y=3, and the side length is just (xq-xp)=(3-1)=2 (base =2) Similarly, RS must also be horizontal with length 2 and along the line y=8. (check) Distance between lines RS and PQ = (yr-ys)=(8-3)=5 (height=5) Area of parallelogram = base * height = 2*5=10
2. This method works for any convex figure with the vertices in order. The vertices PQSR are in order, if we plot them on a graph. Then we write the coordinates of PQSR vertically, and repeat P at the bottom, giving 1,3 3,3 9,8 7,8 1,3 Next, multiply diagonally down on each line and add together (4 times) S1=1*3+3*8+9*8+7*3=3+24+72+21=120 similarly, multiply diagonally up, starting from the second line: S2=3*3+9*3+7*8+1*8=9+27+56+8=100 The area is half of the bigger number less the smaller, Area=(120-100)/2=10
3. By graphing on a square paper, and count squares. Cannot do it here because there is no means to show the graph. You are welcome use this method to check previous calculations.
Since she has $10,000 in coverage, the entire $4000 loss is covered. However, the insurance company would only pay her the amount after the deductible has been taken:
