Question

find the area of the shaded region. the area of the shaded region is 14x (type an exact answer, using π as needed.)

Explanation:

Step1: Determine the radius of the circle

The square has a side length of 14, so the diameter of the circle (which fits perfectly inside the square) is also 14. The radius \( r \) is half of the diameter, so \( r = \frac{14}{2} = 7 \).

Step2: Calculate the area of the circle

The formula for the area of a circle is \( A = \pi r^2 \). Substituting \( r = 7 \) into the formula, we get \( A = \pi (7)^2 = 49\pi \). Wait, but the initial input had a partial answer of \( 14x \), that seems incorrect. Wait, no, looking back, the square has side 14, so diameter of circle is 14, radius 7. Area of circle is \( \pi r^2 = \pi \times 7^2 = 49\pi \). Wait, maybe the initial partial answer was a typo. Let's recheck. The shaded region is the circle inside the square. So side of square is 14, so diameter of circle is 14, radius 7. Area of circle is \( \pi r^2 = \pi \times 7^2 = 49\pi \).

Wait, maybe I misread. Let me check again. The square has side 14, so the circle is inscribed in the square, so diameter = 14, radius = 7. Area of circle is \( \pi r^2 = \pi \times 7^2 = 49\pi \). So the correct area should be \( 49\pi \).

Answer:

\( 49\pi \)