1. **Problem statement:** Calculate the perimeter of a compound shape formed by a rectangle and a sector of a circle. 2. **Given:** - Rectangle length = 37 cm - Rectangle height = 22 cm - Sector radius = 37 cm - Sector angle = 20° 3. **Formula for perimeter:** The perimeter of the compound shape is the sum of: - The two vertical sides of the rectangle (each 22 cm) - The bottom side of the rectangle (37 cm) - The arc length of the sector Note: The top side of the rectangle is replaced by the arc of the sector. 4. **Calculate the arc length of the sector:** The arc length $L$ of a sector with radius $r$ and angle $\theta$ in degrees is given by: $$L = 2 \pi r \times \frac{\theta}{360}$$ Substitute $r=37$ cm and $\theta=20^\circ$: $$L = 2 \pi \times 37 \times \frac{20}{360}$$ 5. **Simplify the arc length:** $$L = 2 \pi \times 37 \times \frac{1}{18} = \frac{74 \pi}{18} = \frac{37 \pi}{9}$$ 6. **Calculate numerical value:** $$L \approx \frac{37 \times 3.1416}{9} \approx \frac{116.238}{9} \approx 12.915$$ cm 7. **Calculate the perimeter:** $$P = 22 + 22 + 37 + 12.915 = 81.915$$ cm 8. **Round to 1 decimal place:** $$P \approx 81.9$$ cm **Final answer:** The perimeter of the compound shape is **81.9 cm**.