The perimeter of the regular octagon which has one side with endpoints (-1,2) and (3,-1) is 40 units.
How to find the perimeter of plane?
The measure of the boundary of a plane or shape is called its perimeter. The perimeter of a plane or shape is the sum of all the sides.
The perimeter of a regular octagon can be calculated with the following formula.
[tex]P=8a[/tex]
Here (a) is the side of the octagon.
A regular octagon has one side with endpoints (-1,2) and (3,-1). Thus, the length of the one side using the distance formula is,
[tex]a=\sqrt{[3-(-1)]^2+[-1-2]^2}\\a=\sqrt{[4]^2+[-3]^2}\\a=\sqrt{16+9}\\a=\sqrt{25}\\a=5[/tex]
Put this value in the above formula to find the perimeter.
[tex]P=8\times5\\P=40\rm\; units[/tex]
Hence, the perimeter of the regular octagon which has one side with endpoints (-1,2) and (3,-1) is 40 units.
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