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A regular hexagon has a perimeter of $p$ (in length units) and an area of $A$ (in square units). If $A = \frac{3}{2},$ then find the side length of the hexagon.

 Feb 15, 2024
 #1
avatar+128732 
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The side length =  p / 6

 

A =  (1/2)(6) (p/6)^2 sin (60°)

 

3/2 = 3 (p^2 / 36) sqrt (3) / 2

 

1 =   sqrt (3) * p^2 / 36

 

36 / sqrt (3) = p^2

 

36/ 3^(1/2)  = p^2         take the +sqrt of both sides

 

p =  6 / 3^(1/4)

 

Side length  =    [ 6/ 3^(1/4)] / 6  = 1/3^(1/4) ≈  .759

 

cool cool cool

 Feb 15, 2024

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