Answer:
The perimeter of the regular octagon is 104 units
Step-by-step explanation:
we know that
The segment LM is the length of one side of the octagon
we have the coordinates
L(-6,-2) and M(6,3)
step 1
Find the distance LM
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[tex]d_L_M=\sqrt{(3+2)^{2}+(6+6)^{2}}[/tex]
[tex]d_L_M=\sqrt{(5)^{2}+(12)^{2}}[/tex]
[tex]d_L_M=\sqrt{169}[/tex]
[tex]d_L_M=13\ units[/tex]
step 2
Find the perimeter
we know that
A regular octagon has eight equal sides
so
To find out the perimeter, multiply by 8 the length of the segment LM
[tex]P=8(13)=104\ units[/tex]
