To find the area of the shaded region where a square is cut out of a circle, we need to go through the following steps:
1. Determine the radius of the circle:
- Given the diameter of the circle is 14 feet, the radius of the circle is half of this:
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{14 \text{ feet}}{2} = 7 \text{ feet}
\][/tex]
2. Calculate the area of the circle:
- The formula for the area of a circle is [tex]\( A = \pi r^2 \)[/tex]. Using [tex]\( \pi = 3.14 \)[/tex] and [tex]\( r = 7 \)[/tex] feet:
[tex]\[
A_{\text{circle}} = 3.14 \times (7^2) = 3.14 \times 49 \approx 153.86 \text{ square feet}
\][/tex]
3. Calculate the area of the square:
- The side length of the square is the same as the diameter of the circle, which is 14 feet. The area of a square is given by [tex]\( A = \text{side}^2 \)[/tex]:
[tex]\[
A_{\text{square}} = 14 \times 14 = 196 \text{ square feet}
\][/tex]
4. Determine the area of the shaded region:
- The shaded region is the area of the circle minus the area of the square:
[tex]\[
A_{\text{shaded}} = A_{\text{circle}} - A_{\text{square}} = 153.86 \text{ square feet} - 196 \text{ square feet} = -42.14 \text{ square feet}
\][/tex]
However, since we are interested in the shaded region where a square is removed from a circle and we end up with a negative area, this indicates that the question might involve understanding the logical area placement. The negative result (-42.14) shows the square's area is somewhat greater than the presented circular one according to given statements, which can bring forward adjustments to understanding dimensions or an overlooked context.
Among the multiple-choice options provided:
- [tex]$25 \text{ ft}^2$[/tex]
- [tex]$40 \text{ ft}^2$[/tex]
- [tex]$30 \text{ ft}^2$[/tex]
- [tex]$80 \text{ ft}^2$[/tex]
None exactly match the calculation (or could be incorrectly interpretted considering dimension resets and practical mixups). The significant hint is that an involved context should place circle-overfitting arrangement, which general results marked intuiitionally verifying:
[tex]\(153.86\neq exact~ circle-fitting among any aforementioned exact approx.\)[/tex].
Thus, semi-accurate choice consideration applies logical assertion when advancing context folds or simplifying and standard classroom intact approximations can assume [tex]\(nearest~ logical~ options\)[/tex].
Thus, [tex]\( standard~ measures \)[/tex]:
[tex]\[
Practical~answer:(-42.14), as negative needs dissect follow-through derivations
thus (closest estimate)= (of-abbreviation-would-considerative dynamics)
n/a.
\][/tex]
Ensuring constructive learning contexts.
