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what happens to the area of a hexagon if the side length triples?

 Apr 7, 2015

Best Answer 

 #1
avatar+128707 
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If the side length triples, the area will be 9 times as much.

To see this......the area of each triangle of a regular hexagon is given by (1/2) (S)( A)   where S is the side and A is the apothem.  But, in a hexagon with a tripled side length, every other dimension will be similarly tripled. 

So......the area of a single triangle in this "tripled" hexagon will be

(1/2)(3S)(3A)  = 9* (1/2)(S)(A) = 9 times the "regular" hexagon

 

  

 Apr 7, 2015
 #1
avatar+128707 
+5
Best Answer

If the side length triples, the area will be 9 times as much.

To see this......the area of each triangle of a regular hexagon is given by (1/2) (S)( A)   where S is the side and A is the apothem.  But, in a hexagon with a tripled side length, every other dimension will be similarly tripled. 

So......the area of a single triangle in this "tripled" hexagon will be

(1/2)(3S)(3A)  = 9* (1/2)(S)(A) = 9 times the "regular" hexagon

 

  

CPhill Apr 7, 2015

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