Welcome back — been a while! Let's pick up where you left off. The question asks to find the area and perimeter of a sector of a circle with a radius of $21$ cm and an angle of $120^\circ$. Given: Radius, $r = 21$ cm Angle, $\theta = 120^\circ$ Step 1: Calculate the area of the sector. The formula for the area of a sector is $A = \frac{\theta}{360^\circ} \times \pi r^2$. $$A = \frac{120^\circ}{360^\circ} \times \frac{22}{7} \times (21 \text{ cm})^2$$ $$A = \frac{1}{3} \times \frac{22}{7} \times 441 \text{ cm}^2$$ $$A = \frac{1}{3} \times 22 \times 63 \text{ cm}^2$$ $$A = 22 \times 21 \text{ cm}^2$$ $$A = 462 \text{ cm}^2$$ The area of the sector is $\boxed{\text{462 cm}^2}$. Step 2: Calculate the perimeter of the sector. The formula for the perimeter of a sector is $P = \frac{\theta}{360^\circ} \times 2\pi r + 2r$. $$P = \frac{120^\circ}{360^\circ} \times 2 \times \frac{22}{7} \times 21 \text{ cm} + 2 \times 21 \text{ cm}$$ $$P = \frac{1}{3} \times 2 \times 22 \times 3 \text{ cm} + 42 \text{ cm}$$ $$P = 44 \text{ cm} + 42 \text{ cm}$$ $$P = 86 \text{ cm}$$ The perimeter of the sector is $\boxed{\text{86 cm}}$. Send me the next one 📸