Question 1182756
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I think both the solutions in the link provided by the other tutor are more complicated than necessary.<br>
Let M be the midpoint of side AB of the original regular hexagon.  Then M is one vertex of the smaller inscribed regular hexagon.<br>
Let O be the center of the two hexagons; draw segments OA and OM; triangle AMO is a 30-60-90 right triangle.<br>
OA and OM are corresponding parts of the two hexagons; the ratio of their lengths is {{{sqrt(3):2}}}; so the ratio of the areas of the two hexagons is 3:4.<br>
ANSWER: 3:4<br>