If the diameter of a semi-circular protractor is 14 cm,

Let AB be the diameter of the semi-circular protractor.

So, $A B=14 \mathrm{~cm}$

We know that perimeter of the semicircle $=\frac{1}{2}(2 \pi r)+2 r$

We have given the diameter of the protractor.

Therefore, radius of the protractor $=\frac{14}{2}$

So, radius of the protractor 

Substituting the value of r in equation (1) we get,

Perimeter of the semi-circular protractor $=\frac{1}{2}(2 \pi \times 7)+2 \times 7$

Perimeter of the semi-circular protractor $=(\pi \times 7)+14$

Substituting $\pi=\frac{22}{7}$ we get,

Perimeter of the semi-circular protractor $=\left(\frac{22}{7} \times 7\right)+14$

Perimeter of the semi-circular protractor $=22+14$

Hence perimeter of the semi-circular protractor $=36$

Therefore, perimeter of the semi-circular protractor is $36 \mathrm{~cm}$.