ANSWER
• Side length = ,40 m
,
• Apothem = ,27.53 m
,
• Area = ,2752.76 m²
EXPLANATION
The perimeter is the sum of the side lengths. SInce this is a regular pentagon, all sides have the same length:
[tex]P=5s[/tex]
The side length is:
[tex]s=\frac{P}{5}=\frac{200m}{5}=40m[/tex]
The apothem is the distance from the center of the pentagon to the side. The formula is:
[tex]a=\frac{s}{2\tan\mleft(\frac{180}{5}\mright)}=\frac{40m}{2\tan 36}\approx27.53m[/tex]
And the area of a pentagon is:
[tex]A=\frac{1}{2}\cdot a\cdot5s=\frac{1}{2}\cdot27.53m\cdot5\cdot40m\approx2752.76m^2[/tex]
