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Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.    

 

The sides are equal and the angles are equal.    

That means the hexagon is a regular hexagon.    

 

                                                                                               3 sqrt(3)    

The area of a regular hexagon in terms of its sides is   A  =  ––––––––  x  a2  where "a" is a side.    

                                                                                                     2    

 

                                                                                       A  =  ( 3 x sqrt(3) x 32 ) / 2       

                                                                                       A  =  ( 27 sqrt(3) ) / 2    

Is that good enough or do you need a number.     

                                                                                       A  =  ( 27 x 1.732 ) / 2     

                                                                                       A  =  23.383    

.   

1 nov 2024