To find the area of the parallelogram defined by the vertices A(3, 0), B(1, 3), C(5, 2), and D(3, 1), we can use the formula for the area based on the coordinates of the vertices.
The area (A) can be calculated using the formula:
A = |(x1(y2 - y4) + x2(y4 - y1) + x3(y1 - y2) + x4(y2 - y3)) / 2|
Substituting the coordinates of points A(3, 0), B(1, 3), C(5, 2), and D(3, 1) into the formula:
A = |(3(3 - 1) + 1(1 - 0) + 5(0 - 3) + 3(3 - 2)) / 2|
Calculating each part:
- 3(3 – 1) = 3 * 2 = 6
- 1(1 – 0) = 1 * 1 = 1
- 5(0 – 3) = 5 * -3 = -15
- 3(3 – 2) = 3 * 1 = 3
Now we combine these results:
A = |(6 + 1 - 15 + 3) / 2|
This simplifies to:
A = |(-5) / 2| = 5 / 2 = 2.5
Thus, the area of the parallelogram is 2.5 square units.