Note: T is the midpoint of PO.
PT = 6x + 4 and TO = 52.

x=8

Step-by-step explanation:

if T is the midpoint of PO then PT=TO

6x+4=52

-4        -4

6x     = 48

:6           :6

x=8

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.