Of course this is a site to learn

Ok so basically we have that

where a is apothem and p is permieter

Now since we know that the exterior angle of a n-gon is

we know due to the linear pair postulate that the interior angle of an n-gon is

so for a pentagon(5-gon)

the interior angle would be

So now we know that the angle at a vertex is 108 we know that the apothem bisects it making

the angle that the apothem cuts off 44...so now we have a right triangle with angles ,90,44,46

So we need to calculate the apothem or in this case we are given it but we need to find sidelenght

so we use trig

and since that gives us half of our side we see that the sidelenghts are

21.75

now we go to our formula

Now since

where n is the sidelength we see that

so now we see