we know that
The formula to find the area of a regular polygon is given by
\(A=\frac{S^{2}*n}{4*tan(\frac{180}{n})}\)
where
s is the length of the side
n is the number of sides
In this problem we have
\(A=6.9\ cm^{2} \\ n=5\)
Solve for S
Find the length of the side of the regular pentagon
\(S^{2} =\frac{1}{n} *[A*4*tan(180/n)]\\ \\ S^{2} =\frac{1}{5} *[6.9*4*tan(180/5)]\\ \\ S^{2}=4.01\\ \\ S=2\ cm\)
Find the perimeter of the regular pentagon
\(Perimeter=5*2=10\ cm\)
therefore
the answer is
the perimeter of the regular pentagon is \(10\ cm\)
