1. **State the problem:** We need to find the area of the blue shaded region in a circle of radius 7 cm, where the sector has a central angle of 150°. The blue region is the sector area minus the triangle formed by the two radii and the chord. 2. **Formulas used:** - Area of sector: $$A_{sector} = \frac{\theta}{360^\circ} \times \pi r^2$$ where $\theta$ is the central angle in degrees and $r$ is the radius. - Area of triangle formed by two radii and the chord: $$A_{triangle} = \frac{1}{2} r^2 \sin(\theta)$$ 3. **Calculate the sector area:** $$A_{sector} = \frac{150}{360} \times \pi \times 7^2 = \frac{5}{12} \times \pi \times 49 = \frac{245}{12} \pi \approx 64.17$$ cm² 4. **Calculate the triangle area:** $$A_{triangle} = \frac{1}{2} \times 7^2 \times \sin(150^\circ) = \frac{1}{2} \times 49 \times 0.5 = 12.25$$ cm² 5. **Find the blue shaded area:** $$A_{blue} = A_{sector} - A_{triangle} = 64.17 - 12.25 = 51.92$$ cm² 6. **Round to the nearest tenth:** $$51.92 \approx 51.9$$ cm² **Final answer:** The area of the blue shaded region is **51.9 cm²**.