Question

In octagon $ABCDEFGH$, every side is perpendicular to each of its adjacent sides. What is the perimeter of $ABCDEFGH$?

Answer 1

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

$P=AB+BC+CD+DE+EF+FG+GH+HA$

we have

$BC=10\ units\\CD=6\ units\\EF=4\ units\\GH=8\ units$

substitute

$P=AB+10+6+DE+4+FG+8+HA$

Combine like terms

$P=AB+DE+FG+HA+28$

we know that

$BC=DE+FG+HA$ ---> by segment addition postulate

$BC=10\ units$

so

$DE+FG+HA=10\ units$

substitute in the expression of perimeter

$P=AB+(DE+FG+HA)+28$

$P=AB+10+28\\P=AB+38$

Since

$DC= 6\ units$

and

$EF = 4\ units$

The distance between F and line BC must be

$6-4=2\ units$

so

$AB = HG + 2 = 10\ units$

substitute

$P=AB+38\\P=10+38=48\ units$