Final answer:
The area of the triangle formed by the points A(6, 9), B(9, 9), and C(9, 4) is 7.5 square units, calculated using the formula for the area of a right-angled triangle. None of the provided answer choices match this value, suggesting there may be an error in the question.
Step-by-step explanation:
To find the area of the polygon defined by the points A(6, 9), B(9, 9), and C(9, 4), we can notice that this polygon is a right-angled triangle. The horizontal leg of the triangle is the distance between A and B, which can be found by taking the difference of the x-coordinates of B and A (9 - 6 = 3 units). The vertical leg of the triangle is the distance between B and C, found by taking the difference of the y-coordinates of B and C (9 - 4 = 5 units). Therefore, the area of the triangle can be calculated using the formula for the area of a right-angled triangle, which is 1/2 * base * height. Substituting the lengths we found, the calculation would be:
Area = 1/2 * 3 units * 5 units = 7.5 square units
However, since this value is not an option provided, and there may be an error in the question as no matching answer choice is given, we should double-check the original problem or perhaps consider that the question contains an error.