Final answer:
The area of the shaded region in a rectangle with an inscribed circle is found by subtracting the area of the circle from the area of the rectangle. Calculate the area of the rectangle using length times width, and the area of the circle using π times the radius squared. The difference between the two provides the shaded area, rounded to the appropriate number of significant figures.
Step-by-step explanation:
To calculate the area of the shaded region inside a rectangle when a circle is drawn within it, subtract the area of the circle from the area of the rectangle. The formula to determine the area of a circle is A = πr², where r is the radius of the circle. The formula for the area of a rectangle is the product of its length and width.
Let's assume the radius of the circle is d1 cm, thus the area of the circle is π(d1²). The rectangle's dimensions are given as d3 cm by 3d3 cm, making the rectangle's area d3 × 3d3 cm². To find the area of the shaded region, we calculate the area of the rectangle and subtract the area of the circle: Area of the shaded region = (d3 × 3d3) - π(d1²).
Without the specific values for d1 and d3, we cannot provide a numerical answer, but this formula will give the area of the shaded region once the values are known. Round according to significant figures provided by the respective measurements.