Question

6. Given perimeter of 200 m, determine each side of a regularpentagon, find apothem, then find area.

Answer 1

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:

$P=5s$

The side length is:

$s=\frac{P}{5}=\frac{200m}{5}=40m$

The apothem is the distance from the center of the pentagon to the side. The formula is:

$a=\frac{s}{2\tan\mleft(\frac{180}{5}\mright)}=\frac{40m}{2\tan 36}\approx27.53m$

And the area of a pentagon is:

$A=\frac{1}{2}\cdot a\cdot5s=\frac{1}{2}\cdot27.53m\cdot5\cdot40m\approx2752.76m^2$