Final answer:
The largest size of a rectangle inscribed in a semicircle of radius 1 unit, with two vertices on the diameter, has an area of 2 square units, which is the width (equal to the semicircle's diameter) multiplied by the maximum height (equal to the semicircle's radius).
Step-by-step explanation:
To find the largest size of a rectangle that can be inscribed in a semicircle of radius 1 unit, we should recall that such a rectangle will have its two vertices on the diameter and the other two vertices touching the semicircle. In this configuration, the rectangle's width will be equal to the diameter of the semicircle and hence is 2 units (since the semicircle's radius is 1 unit). The height of the rectangle will be less than the semicircle's radius because the rectangle is fit within the semicircle, meaning that the maximum height is 1 unit, the radius itself, when the rectangle's top vertices touch the semicircle at its midpoint.
Therefore, the largest area of the rectangle, using the formula for the area of a rectangle (A = width × height), is A = 2 × 1 = 2 square units. This corresponds to answer choice C) 2 square units, which is the maximum inscribed rectangle area that can be achieved within a semicircle of radius 1.