1. **Problem statement:** Find the area of the shaded triangle inside a circle with radius 12 cm and central angle 47°. 2. **Formula for the area of a triangle with two sides and included angle:** $$\text{Area} = \frac{1}{2}ab\sin(C)$$ where $a$ and $b$ are the sides and $C$ is the included angle. 3. **Given:** - $a = 12$ cm - $b = 12$ cm - $C = 47^\circ$ 4. **Calculate the area:** $$\text{Area} = \frac{1}{2} \times 12 \times 12 \times \sin(47^\circ)$$ 5. **Simplify:** $$= \frac{1}{2} \times 144 \times \sin(47^\circ)$$ 6. **Calculate $\sin(47^\circ)$:** $$\sin(47^\circ) \approx 0.7314$$ 7. **Substitute:** $$\text{Area} = 72 \times 0.7314 = 52.6608$$ 8. **Round to nearest hundredth:** $$\boxed{52.66 \text{ cm}^2}$$ This is the area of the shaded triangle.