Question

A circle is placed in a square with side length of 14 ft, as shown below. Find the area of the shaded region. Use the value 3.14 for pie, and do not round your answer. Be sure to include the correct unit in your answer

Answer 1

To find the area of the shaded region, we need to determine the area of the square and the area of the circle, then subtract the area of the circle from the area of the square.

1. **Area of the Square**:
The side length of the square is given as 14 ft.
The area of a square is calculated using the formula:
\[
\text{Area of square} = \text{side}^2 = 14^2 = 196 \text{ ft}^2
\]

2. **Area of the Circle**:
The diameter of the circle is equal to the side length of the square, which is 14 ft. Thus, the radius \( r \) of the circle is:
\[
r = \frac{\text{diameter}}{2} = \frac{14}{2} = 7 \text{ ft}
\]
The area of a circle is calculated using the formula:
\[
\text{Area of circle} = \pi r^2
\]
Substituting \( \pi \) with 3.14 and \( r = 7 \text{ ft} \):
\[
\text{Area of circle} = 3.14 \times 7^2 = 3.14 \times 49 = 153.86 \text{ ft}^2
\]

3. **Area of the Shaded Region**:
Now, we subtract the area of the circle from the area of the square:
\[
\text{Area of shaded region} = \text{Area of square} - \text{Area of circle} = 196 \text{ ft}^2 - 153.86 \text{ ft}^2 = 42.14 \text{ ft}^2
\]

Thus, the area of the shaded region is \( \boxed{42.14 \text{ ft}^2} \).