Final answer:
The area of the shaded region can be found using the formula A = πr², with the result reflecting the number of significant figures in the given radius. Estimations can be made based on the geometrical relationships when exact measures are not available.
Step-by-step explanation:
To find the area of the shaded region, you need to know the formula for the area of a circle, which is A = πr². This formula indicates that the area (A) is equal to pi (π), approximately 3.1415927, multiplied by the radius (r) of the circle squared. When a problem provides you with the radius, you can simply plug the value into this formula. If working with significant figures, it is important to present the final answer with the appropriate number of significant figures based on the given data.
For example, if the radius of a circle is given as 1.2 meters, the calculation would be A = π(1.2 m)² = 4.5238934 m², leading to a rounded answer of A=4.5 m² due to the radius having two significant figures. In related scenarios, understanding the relationship between area and radius can assist you in estimating the area within certain geometrical constraints, such as a circle within a square.