Question

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

Answer 1

• Side length = ,40 m

,

• Apothem = ,27.53 m

,

• Area = ,2752.76 m²

Step-by-step 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=(P)/(5)=(200m)/(5)=40m`

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

`a=(s)/(2\tan\mleft((180)/(5)\mright))=(40m)/(2\tan 36)\approx27.53m`

And the area of a pentagon is:

`A=(1)/(2)\cdot a\cdot5s=(1)/(2)\cdot27.53m\cdot5\cdot40m\approx2752.76m^2`