In circle D with \( m \angle C D E=144^{\circ} \) and \( C D=4 \), find the area of sector CDE. Round to the nearest hundredth.

To find the area of sector CDE, we can use the formula for the area of a sector, which is given by: \[ \text{Area} = \frac{\theta}{360^{\circ}} \times \pi r^2 \] where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle. Given that \(m \angle CDE = 144^{\circ}\) and \(CD = 4\) (which acts as the radius), we can plug in the values: \[ \text{Area} = \frac{144}{360} \times \pi \times 4^2 \] Calculating \(4^2\): \[ 4^2 = 16 \] Now substituting this into the area formula: \[ \text{Area} = \frac{144}{360} \times \pi \times 16 \] To simplify \(\frac{144}{360}\): \[ \frac{144}{360} = \frac{2}{5} \] Now substituting back into the formula: \[ \text{Area} = \frac{2}{5} \times \pi \times 16 \] Now calculating this: \[ \text{Area} = \frac{32\pi}{5} \] Using \(\pi \approx 3.14\): \[ \text{Area} = \frac{32 \times 3.14}{5} \approx \frac{100.48}{5} \approx 20.096 \] Rounding to the nearest hundredth: \[ \text{Area} \approx 20.10 \] Therefore, the area of sector CDE is approximately \(20.10\) square units.