Answer:
Area of a regular pentagon(A) is given by:
\(A=\frac{1}{4}(\sqrt{5(5+2\sqrt{5}}) s^2\)
where, s is the side of the regular pentagon
As per the statement:
The area of the regular pentagon is 6.9 cm^2.
⇒A = 6.9 cm^2
then;
\(6.9=\frac{1}{4}(\sqrt{5(5+2\sqrt{5}}) s^2\)
Multiply both sides by 4 we have;
\(27.6=\sqrt{5(5+2\sqrt{5}}s^2\)
Simplify:
\(27.6 = \sqrt{47.3606798}s^2\)
⇒\(27.6 = \sqrt{47.3606798}s^2\)
Divide both sides by \(\sqrt{47.3606798}\) we have;
\(4.01051475= s^2\)
⇒\(\sqrt{4.01051475}=s\)
⇒2.00262696 cm = s
or
s = 2.00262696 cm
Perimeter of the regular pentagon(P) is given by:
\(P=5s\)
then;
\(P = 5 \cdot 2.00262696 = 10.0131348 cm\)
Therefore, the perimeter is, 10.0131348 cm
