Questions: Find the area of the shaded region above. (The figure is not drawn to scale and remember to use π ≈ 3.14 for all calculations involving π ). Area = □ km^2 Round answers to 2 decimal places as needed.

Find the area of the shaded region above. (The figure is not drawn to scale and remember to use π ≈ 3.14 for all calculations involving π ).

Area = □ km^2
Round answers to 2 decimal places as needed.

Transcript text: Find the area of the shaded region above. (The figure is not drawn to scale and remember to use $\pi \approx 3.14$ for all calculations involving $\pi$ ). Area $=$ $\square$ $\mathrm{km}^{2}$ Round answers to 2 decimal place as needed.

Solution

Solution Steps

Step 1: Calculate the Area of the Full Circle

The radius of the circle is given as 5 km. The formula for the area of a circle is $ A = \pi r^2 $.

Using $ \pi \approx 3.14 $ and $ r = 5 $ km: \[ A = 3.14 \times (5)^2 \] \[ A = 3.14 \times 25 \] \[ A = 78.5 \text{ km}^2 \]

Step 2: Determine the Fraction of the Circle that is Shaded

The shaded region represents a quarter of the circle (as indicated by the diagram).

Step 3: Calculate the Area of the Shaded Region

Since the shaded region is a quarter of the full circle, we divide the area of the full circle by 4: \[ \text{Shaded Area} = \frac{78.5}{4} \] \[ \text{Shaded Area} = 19.625 \text{ km}^2 \]