We are given a square with a side length of 14 mm, and a circle is inscribed within it. We are tasked with finding the area of the shaded region, which is the area outside the circle but inside the square.

Steps to solve:

1. Area of the square: The side length of the square is $14 \, \text{mm}$. $\text{Area of square} = \text{side}^2 = 14^2 = 196 \, \text{mm}^2$

2. Area of the circle: The diameter of the circle is equal to the side length of the square, which is $14 \, \text{mm}$. Therefore, the radius $r$ of the circle is half of the diameter: $r = \frac{14}{2} = 7 \, \text{mm}$ The area of the circle is given by: $\text{Area of circle} = \pi r^2 = 3.14 \times 7^2 = 3.14 \times 49 = 153.86 \, \text{mm}^2$

3. Area of the shaded region: The shaded region is the difference between the area of the square and the area of the circle: $\text{Area of shaded region} = \text{Area of square} - \text{Area of circle}$ $\text{Area of shaded region} = 196 - 153.86 = 42.14 \, \text{mm}^2$

Thus, the area of the shaded region is 42.14 mm².

Would you like any further clarification or details?

Related questions:

1. How would the area of the shaded region change if the side of the square were doubled?
2. How can you calculate the circumference of the circle?
3. What is the ratio of the area of the circle to the area of the square?
4. How would the solution differ if the circle were circumscribed around the square instead of inscribed?
5. How does using a more precise value of $\pi$ affect the result?

Tip:

Always ensure the correct units are used, especially when working with areas, as forgetting to square units is a common mistake.