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