Question

find the area of the shaded region of circle v below. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Determine radius and angle

Radius \( r = 7 \), central angle \( \theta = 90^\circ \)

Step2: Calculate sector area

Sector area \( = \frac{\theta}{360^\circ} \pi r^2 = \frac{90^\circ}{360^\circ} \pi (7)^2 = \frac{49}{4}\pi \approx 38.48 \)

Step3: Calculate triangle area

Triangle area \( = \frac{1}{2} r^2 = \frac{1}{2} (7)^2 = 24.5 \)

Step4: Find shaded area (segment)

Shaded area \( = \text{Sector area} - \text{Triangle area} \approx 38.48 - 24.5 = 13.98 \approx 14.0 \)

Answer:

14.0