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If the radius of smaller circle is r cm, by inspection

2r + 4* 2r = 18

10r = 18

r = 1.8 

Perimeter of the figure = half perimeter of big circle + full perimeter of small circle + diameter of big circle + 2* diameter of small circle

= 1/2 * 2 * π* 4 * 1.8 + 2 * π* 1.8 + 2 * 4 * 1.8 + 2 * 2 * 1.8 cm

= 12.56 + 11.304 + 14.4 + 7.2 cm

= 45.464 cm

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