uh for part a the ans is 13.3cm

Ok, let me confirm again, likely a miscalculation of an angle on my wnd

I have gone through my angle workings and found no error with my angle calculations.

I used Desmos online to do my calculations rather than a physical calculator.

The subsequent arc length calculations also did not seem to show an error.

(Arc length formula for radian format is r0, so the perimeter of the shaded region is just that arc length plus the 3 cm and 5 cm lengths)

Check the answer key again, but I still believe it's 13.9 cm.

(My workings could still be incorrect, but there are cases of answer keys being incorrect as well)

I used a different online "cosine rule calculator" and confirmed that the angle in question is 0.981765 rad radians, so 6 x 0.981765 + 3 + 5 is approximately 13.9 cm.

13.3 cm given by the answer key seems wrong.

ohk thx