To find the area of the shaded region, which consists of a square with a circular section cut out of it, follow these steps:

1. Find the area of the square:

   • The side length of the square is given as 10 feet.
   • The area of a square is calculated by squaring the side length. $\text{Area of square} = 10 \times 10 = 100 \text{ square feet}$

2. Find the area of the circle:

   • The diameter of the circle is equal to the side length of the square, which is 10 feet.
   • Thus, the radius $r$ of the circle is half of the diameter: $r = \frac{10}{2} = 5 \text{ feet}$
   • The area of a circle is given by $\pi r^2$.
   • Using $\pi \approx 3.14$: $\text{Area of circle} = 3.14 \times (5)^2 = 3.14 \times 25 = 78.5 \text{ square feet}$

3. Calculate the area of the shaded region:

   • Subtract the area of the circle from the area of the square: $\text{Shaded area} = \text{Area of square} - \text{Area of circle} = 100 - 78.5 = 21.5 \approx 22 \text{ square feet}$

Answer:

The area of the shaded region is approximately 22 square feet.

Would you like a breakdown of any particular part of this solution?

Here are some additional related questions you might find interesting:

1. How would the shaded area change if the square's side length increased?
2. What would the shaded area be if the circle's radius was reduced by half?
3. If the value of π was used as 3.1416, how would it affect the result?
4. What would the area of the circle be if the square’s side length was doubled?
5. How would the shaded area change if we used a rectangle instead of a square?

Tip: Always check if the units are consistent in area calculations to avoid errors in the final answer.