Answer:
The perimeter is 48 units
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The perimeter of the octagon is the sum of its length sides
so
[tex]P=AB+BC+CD+DE+EF+FG+GH+HA[/tex]
we have
[tex]BC=10\ units\\CD=6\ units\\EF=4\ units\\GH=8\ units[/tex]
substitute
[tex]P=AB+10+6+DE+4+FG+8+HA[/tex]
Combine like terms
[tex]P=AB+DE+FG+HA+28[/tex]
we know that
[tex]BC=DE+FG+HA[/tex] ---> by segment addition postulate
[tex]BC=10\ units[/tex]
so
[tex]DE+FG+HA=10\ units[/tex]
substitute in the expression of perimeter
[tex]P=AB+(DE+FG+HA)+28[/tex]
[tex]P=AB+10+28\\P=AB+38[/tex]
Since
[tex]DC= 6\ units[/tex]
and
[tex]EF = 4\ units[/tex]
The distance between F and line BC must be
[tex]6-4=2\ units[/tex]
so
[tex]AB = HG + 2 = 10\ units[/tex]
substitute
[tex]P=AB+38\\P=10+38=48\ units[/tex]
