1. **State the problem:** We need to find the area of the blue shaded region, which is the area of a right triangle minus the area of a circle inside it. 2. **Given:** The right triangle has legs of length 20 cm each. The circle inside has a radius of 4 cm. 3. **Formula for the area of a right triangle:** $$\text{Area}_{\triangle} = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2$$ 4. **Calculate the area of the triangle:** $$\text{Area}_{\triangle} = \frac{1}{2} \times 20 \times 20 = \frac{1}{2} \times 400 = 200 \text{ cm}^2$$ 5. **Formula for the area of a circle:** $$\text{Area}_{circle} = \pi r^2$$ 6. **Calculate the area of the circle:** $$\text{Area}_{circle} = \pi \times 4^2 = \pi \times 16 = 16\pi \text{ cm}^2$$ 7. **Calculate the area of the blue shaded region:** $$\text{Area}_{blue} = \text{Area}_{\triangle} - \text{Area}_{circle} = 200 - 16\pi$$ 8. **Approximate the value using $\pi \approx 3.1416$:** $$16 \times 3.1416 = 50.2656$$ $$\text{Area}_{blue} \approx 200 - 50.2656 = 149.7344 \text{ cm}^2$$ 9. **Round to the nearest hundredth:** $$149.73 \text{ cm}^2$$ **Final answer:** The area of the blue shaded region is approximately $149.73$ cm$^2$.