Radius (r_{1}) of gold region (i.e., 1^{st} circle)

Given that each circle is 10.5 cm wider than the previous circle.

Therefore, radius (r_{2}) of 2^{nd} circle = 10.5 + 10.5 21 cm

Radius (r_{3}) of 3^{rd} circle = 21 + 10.5

= 31.5 cm

Radius (r_{4}) of 4^{th} circle = 31.5 + 10.5

= 42 cm

Radius (r_{5}) of 5^{th} circle = 42 + 10.5

= 52.5 cm

Area of gold region = Area of 1^{st} circle

Area of red region = Area of 2^{nd} circle − Area of 1^{st} circle

Area of blue region = Area of 3^{rd} circle − Area of 2^{nd} circle

Area of black region = Area of 4^{th} circle − Area of 3^{rd} circle

Area of white region = Area of 5^{th} circle − Area of 4^{th} circle

Therefore, areas of gold, red, blue, black, and white regions are 346.5 cm^{2}, 1039.5 cm^{2}, 1732.5 cm^{2}, 2425.5 cm^{2}, and 3118.5 cm^{2 }respectively.