1. **Problem Statement:** Find the area of the shaded part of the door, which is a circular area with diameter 2 ft inside a door of width 4 ft and height 10 ft. 2. **Formula Used:** The area of a circle is given by $$A = \pi r^2$$ where $r$ is the radius. 3. **Important Rules:** The radius is half the diameter. Here, diameter $d = 2$ ft, so radius $r = \frac{2}{2} = 1$ ft. 4. **Intermediate Work:** Calculate the area of the circle: $$A = \pi \times 1^2 = \pi$$ 5. **Explanation:** The shaded part is a circle with radius 1 ft, so its area is simply $\pi$ square feet. 6. **Final Answer:** The area of the shaded part of the door is $$\pi \approx 3.1416$$ square feet.