Question

Find the area of the shaded region.
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Part 1
14
14



A circle is inscribed in a square that has a side of length 14. The circle is shaded.
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Part 1
  
enter your response here square units
​(Type an exact answer in terms of pi​.)

Answer 1

To find the area of the shaded region, which is the area of the circle inscribed in a square, we will follow these steps:

1. **Determine the radius of the circle**:
Since the circle is inscribed in the square, its diameter is equal to the side length of the square. The side length of the square is given as 14 units.

Therefore, the diameter of the circle is 14 units, which means the radius \( r \) of the circle is:
\[
r = \frac{14}{2} = 7 \text{ units}
\]

2. **Calculate the area of the circle**:
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]

Substituting the radius:
\[
A = \pi (7)^2 = \pi \cdot 49 = 49\pi \text{ square units}
\]

Thus, the area of the shaded region (the area of the inscribed circle) is:

\[
\boxed{49\pi} \text{ square units}
\]