Final answer:
The problem involves finding the value of 'a' for an isosceles trapezoid on a parabola. Points J and M are on the x-axis and we use the parabolic equation y = a(x - 1)(x - 5), but additional information is needed to solve for 'a'.
Step-by-step explanation:
The problem deals with an isosceles trapezoid on a parabolic curve. To find the value of a in the equation y = a(x - 1)(x - 5), we need to apply the properties of an isosceles trapezoid and the given conditions that points J and M lie on the x-axis (implying that y=0 for these points). Since the height of the trapezoid is 2 units and the vertices lie on the parabola, we can set up the equation y = a(x - 1)(x - 5) and evaluate it for the relevant x-values where y=0. This will give us two x-values (the bases of the trapezoid), and knowing the height, we can calculate the area of the trapezoid. However, it's only when we know the specific coordinates of J and M or the length of the upper and lower bases that we can solve for 'a'. As the question seems incomplete (it's cut off), we lack enough information to definitively find 'a'. This approach to the problem would allow us to solve for 'a' if the additional necessary information were provided.