Final answer:
To find the area of a parallelogram with given vertices, we can use the formula A = base * height. By calculating the distance between the vertices, we can determine the base and the height of the parallelogram. Substituting the values into the formula, we can find the area.
Step-by-step explanation:
To find the area of a parallelogram, we can use the formula A = base * height. First, let's determine the base and height of the parallelogram. We can find the length of the base by calculating the distance between points (5,5) and (9,10), which is √[(9-5)^2 + (10-5)^2] = √(16+25) = √41. To find the height, we need to find the distance between a point on the base and the opposite side of the parallelogram. Let's take the point (7,6) and find its distance to the line passing through (5,5) and (9,10). Using the point-to-line distance formula, the height is given by |(7-5)(5-10) - (6-5)(5-9)| / √(5-9)^2 + (10-5)^2 = 1.2.
Now we can substitute the base and height into the area formula: A = base * height = √41 * 1.2 = 1.2√41. Therefore, the area of the parallelogram is approximately 1.2√41 square units.