The area (in $$m^2$$) of a circular path of uniform width x metres surrounding a circular region of diameter d metres is ......

Radius of the circular region = $$\frac{Diameter}{2} = \frac{d}{2}$$

Area of the circular region = $$\pi r^2 = \pi \times (\frac{d}{2})^2$$

Radius of the whole circular region include the path = $$\frac{d}{2} +x$$

Area of the whole circular region include the path = $$\pi r^2 = \pi \times (\frac{d}{2} +x)^2$$

Area of the circular path = Area of the whole circular region include the path - Area of the circular region

= $$\pi \times (\frac{d}{2} +x)^2 - \pi \times (\frac{d}{2})^2 = \pi((\frac{d}{2})^2 + x^2 + dx - (\frac{d}{2})^2 )$$

=$$\pi x(x + d)$$