Final answer:
The area of the polygon, a right-angled triangle, is found using the formula (base × height) / 2. With both the base and height as 6 units, the area calculates to 18 square units.
Step-by-step explanation:
The question asks to find the area of a polygon bounded by the lines y = x, x = 6, and the x-axis. This polygon is actually a right-angled triangle with one vertex on the origin (0,0), one vertex on the x-axis (6,0), and one vertex where y = x intersects x = 6, which is at the point (6,6).
To find the area of a triangle, you use the formula area = (base × height) / 2. In this case, our base and height are both equal to 6 units since the line y = x means that for every x, y is equivalent. So, the area is (6 × 6) / 2, which equals 18 square units.
Therefore, the correct answer is a) 18 square units.