To do this question, we draw lines BF and OF. Since ABO represents a quadrant where B is the centre of the quadrant and angle ABO = 90 degrees, it follows that BA, BO and BF are all radii of this quadrant, with length 2 cm.

Similarly, OB = OF = 2 cm since they are radii to the semicircle.

BF = 2 cm, OF = 2 cm, OB = 2 cm

Triangle OBF must be an equilateral triangle.

Angle OBF must be 60 deg. Since angle ABO is 90 deg, angle ABF must be 30 deg.

We use the arc length formula to get minor arc AF and multiply this by 4 to obtain the curved lengths of the cat face ABCDEF. Add this to the straight lengths and there you go, the outer perimeter.