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avatar+1234 

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 $IJKLMN$.

 Jun 14, 2024
 #1
avatar+129733 
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We will have 6 congruent triangles with sides of 3 and an included angle of 60°

 

Area  = 6 (1/2) (3^2) * sin 60  =

 

6 (1/2) (3^2) * sqrt (3)  / 2

 

27 * sqrt (3) / 2  =

 

13.5 *sqrt (3)  ≈ 23.4

 

cool cool cool

 Jun 14, 2024

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