Question 1008892
This is a decagon, whose interior angles are 36 degrees each.
Hard to draw the triangle here, but to determine the length of the apothem, you need the leg of a right triangle whose other leg is 2.5 in and has angles of 18 and 72 degrees.
Call the apothem, a.  Then we have
a/2.5 = tan 72
a = 2.5 tan 72 = 7.69 inches