Answer:
Perimeter of platter is 39.84 inch.
Area of platter is

Explanation:
Apothem is the perpendicular line from center to the side of the octagon. Given that apothem is 6 inch that is AB=6 inch and
(Refer attachment).
Assume DB = BC = x.
Since
is central angle, Therefore


Since apothem AB bisects angle DAC. So,



To find the value of BC, use trigonometry ratio for tan for
,



Solving for x multiply whole equation by 6.


Now, DC = DB + BC



Therefore, side of octagon is 4.98 inch .
Perimeter of octagon is,

Since octagon has 8 sides, so number of side is 8


Therefore, perimeter of platter is 39.84 inch.
Area of octagon is,



Therefore, area of platter is

Note: Values are calculated using two decimal places)