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 $IJKLMN$.

kittykat Dec 24, 2023

#1**0 **

Since all interior angles of the hexagon are equal, each interior angle measures 6(6−2)⋅180∘=120∘. Let P be the center of the hexagon. Then triangle IPJ is equilateral with side length 3, so its area is 43⋅32=493.

The hexagon consists of six such equilateral triangles, so its area is 6⋅493=2273.

BuiIderBoi Dec 24, 2023