formula for area of an octagon is
A=2(1+sqrt(2))a^2 with a being length of a side
so A=2(1+sqrt(2))4.6^2 = 102.12 sq ft
The area of the given octagon is 102.1689 square feet.
A regular octagon is a two-dimensional geometrical figure that has eight equal sides and eight vertices.
Given, the radius of the octagon is 6 feet.
Side length of the octagon(a) is 4.6 feet.
Therefore, the area of the given octagon is
[tex]= 2(1+\sqrt{2})a^{2} \\[/tex] square units
[tex]= 2(1+\sqrt{2})(4.6)^{2}[/tex] square feet
[tex]= (2)(1+1.4142)(21.16)[/tex] square feet
[tex]= (2)(2.4142)(21.16)[/tex] square feet
[tex]= 102.1689[/tex] square feet
Learn more about a regular octagon here: https://brainly.com/question/4412809
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