1. **State the problem:** We have a right triangle with base $30$ units and height $12$ units, and a circle inside it with radius $8$ units. We need to find: - Area of the outside (triangle) - Area of the inside (circle) - Area of the shaded region (triangle minus circle) 2. **Formula for area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Calculate area of the triangle:** $$\text{Area}_{\text{triangle}} = \frac{1}{2} \times 30 \times 12 = \frac{1}{2} \times 360 = 180$$ 4. **Formula for area of a circle:** $$\text{Area} = \pi r^2$$ 5. **Calculate area of the circle:** $$\text{Area}_{\text{circle}} = \pi \times 8^2 = \pi \times 64 = 64\pi$$ 6. **Calculate area of the shaded region:** $$\text{Area}_{\text{shaded}} = \text{Area}_{\text{triangle}} - \text{Area}_{\text{circle}} = 180 - 64\pi$$ 7. **Summary of answers:** - Area of outside (triangle) = $180$ - Area of inside (circle) = $64\pi$ - Area of shaded region = $180 - 64\pi$ This completes the solution.