1. **State the problem:** We need to find the perimeter of the shaded ring sector KLNM formed between two circular arcs with central angle 113° and radii 24 cm (outer) and 15 cm (inner). 2. **Formula for arc length:** The length of an arc is given by $$\text{Arc length} = r \times \theta$$ where $r$ is the radius and $\theta$ is the central angle in radians. 3. **Convert angle to radians:** Given angle is 113°. $$\theta = 113^\circ \times \frac{\pi}{180^\circ} = \frac{113\pi}{180}$$ 4. **Calculate outer arc length (OLM):** $$L_{outer} = 24 \times \frac{113\pi}{180} = \frac{24 \times 113 \pi}{180} = \frac{2712 \pi}{180} = 15.0667\pi$$ 5. **Calculate inner arc length (OKN):** $$L_{inner} = 15 \times \frac{113\pi}{180} = \frac{15 \times 113 \pi}{180} = \frac{1695 \pi}{180} = 9.4167\pi$$ 6. **Calculate the lengths of the two radii (straight lines):** These are simply the difference between points K and L, and points M and N, which are radii of the circles: $$OK = 15 \text{ cm}, \quad OL = 24 \text{ cm}$$ 7. **Perimeter of the shaded shape KLNM:** It consists of the outer arc + inner arc + two radii: $$P = L_{outer} + L_{inner} + OK + OL$$ Substitute values: $$P = 15.0667\pi + 9.4167\pi + 15 + 24 = (15.0667 + 9.4167)\pi + 39 = 24.4834\pi + 39$$ 8. **Calculate numerical value:** $$P = 24.4834 \times 3.1416 + 39 = 76.89 + 39 = 115.89 \text{ cm}$$ 9. **Final answer rounded to 2 decimal places:** $$\boxed{115.89 \text{ cm}}$$