What the question means isÂ
Regular pentagon A is a larger regular pentagon B, in such a way that
the apothem of A coincides with the "radius" of pentagon B, which is actually the distance from the centre to a vertex of B.
The figure attached shows the situation, where regular pentagon A is the lighter figure, and pentagon B is the darker one inside A.
The ratio of the areas depends on the ratio of the apothems.
The ratio of an apothem to the "radius" is the ratio sin(108/2)=sin(54), since the interior angle of a pentagon is 108 degrees.
The ratio of areas of B to A is the square of the ratio of the apothems, namely sin^2(54)=0.809017^2=0.654508
