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Answer :
The area of each of the five scoring regions are as under :
For Gold : \(\pi (10.5)^2 \)
\( = \ \frac{22}{7} × 110.25 \)
\( = \ \frac{2425.5}{7} \ \)
\( = \ 346.5 \ cm^2\)
For Red : \( \pi [ (21)^2 \ - \ (10.5)^2 ] \ \)
\( = \ \frac{22}{7}(441 \ - \ 110.25) \ \)
\( = \ \frac{22}{7} × 330.75 \)
\(= \ \frac{7276.5}{7} \ \)
\( = \ 1039.5 \ cm^2 \)
For Blue : \( \pi [(31.5)^2 \ - \ (21)^2] \ \)
\( = \ \frac{22}{7}(992.25 \ - \ 441) \)
\( = \ \frac{22}{7} × 551.25 \ \)
\( = \ \frac{12127.5}{7} \ \)
\( = \ 1732.5 \ cm^2 \)
For Black : \( \pi [(42)^2 \ - \ (31.5)^2] \ \)
\( = \ \frac{22}{7} (1764 \ - \ 992.25) \)
\( = \ \frac{22}{7} × 771.75 \ \)
\( = \ \frac{16978.5}{7} \ \)
\( = \ 2425.5 \ cm^2 \)
For White : \( \pi [(52.5)^2 \ - \ (42)^2] \ \)
\( = \ \frac{22}{7} (2756.25 \ - \ 1764) \)
\(= \ \frac{22}{7} × 992.25 \ \)
\( = \ \frac{21829.5}{7} \ \)
\( = \ 3118.5 \ cm^2 \)