1. The problem is to understand and simplify the expression $\frac{\theta}{360} \times \pi r^2$. 2. This formula calculates the area of a sector of a circle, where $\theta$ is the central angle in degrees, and $r$ is the radius of the circle. 3. The full area of a circle is given by the formula $\pi r^2$. 4. Since the sector is a fraction of the full circle, the fraction of the circle's area is $\frac{\theta}{360}$ because there are 360 degrees in a full circle. 5. Multiplying the fraction of the circle by the total area gives the sector area: $$\text{Sector Area} = \frac{\theta}{360} \times \pi r^2$$ 6. This formula is used to find the area of a slice of the circle defined by the angle $\theta$. 7. To use it, plug in the values of $\theta$ and $r$ and simplify. Example: If $\theta = 90$ degrees and $r = 3$, then $$\text{Sector Area} = \frac{90}{360} \times \pi \times 3^2 = \frac{1}{4} \times \pi \times 9 = \frac{9\pi}{4}$$ This is the area of a quarter circle with radius 3. Final answer: The expression $\frac{\theta}{360} \times \pi r^2$ gives the area of a sector of a circle with central angle $\theta$ and radius $r$.