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Find the area of each regular polygon. Round to the nearest tenth.

 

1.  an equilateral triangle with an apothem of 2 ft.

2. a regular dodecagon with a side length of 5 m. 

Mathisfornerds  Apr 22, 2018
 #1
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1.  The  apothem  =   side  / (2√3)

So

2  = side / (2√3)     multiply both sides by 2√3

2* 2√3   =  side  =   4√3   =   √48

 

So....the area is given by

 

(1/2) (√48)^2 * √3 / 2  =

 

(1/4) 48√3  =

 

12√3  ft^2    ≈  20.8 ft^2

 

 

 

2. a regular dodecagon with a side length of 5 m.

 

The area   is given by :

 

3 ( 2 + √3) * side^2  =   3 ( 2 + √3) * 5^2   =  3 (2 + √3) * 25  =

 

75 ( 2 + √3)  m^2   ≈  279.9 m^2

 

 

cool cool cool

CPhill  Apr 22, 2018

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