Final answer:
The area of the shaded portion of a circle can be approximated by using the formula πr² if the radius 'r' or diameter 'a' of the circle is known. Since the circle is inscribed in a square, the circle's area is less than that of the square, which is 4r², but more than half of it.
Step-by-step explanation:
To determine the area of the shaded portion of a circle, we first need to understand the formula for the area of a circle, which is πr², where 'r' represents the radius of the circle. According to the reference information provided, we can deduce that if a square has a side length of 'a', and a circle is inscribed within that square, the diameter of the circle is equal to the side length of the square (a = 2r). Therefore, the area of the square is a², which is equivalent to 4r². The area of the circle, being πr², is roughly three-quarters of the square's area since the area of the circle is less than the square but more than its half. Hence, the area of the circle is more than 3r² but less than 4r², approximating it to πr².
Without the specific measurements of the circle or the square, we cannot provide an exact answer from the options given (a-d). However, the logic outlined above should enable the student to calculate the area of the shaded portion of the circle if the radius or diameter is known.