Finding the Area of a Hexagon?

I need help finding the area of a hexagon with an apothem of 6m. Please show/describe work. Thanks. or:I need help finding the area of a hexagon with

I need help finding the area of a hexagon with an apothem of 6m. Please show/describe work. Thanks.

or:I need help finding the area of a hexagon with an apothem of 6m. Please show/describe work. Thanks.

or:Well, luckily, having an apothem means it's a regular solid, and luckier, a regular hexagon can be subdivided into 6 equilateral trianglesThe apothem is a perpendiular bisector of the side of the hexagon and also makes a 30\u00b0 angle with the subdivided triangles. This means you could figure out the sides of the equilateral triangle and hence the sides of the hexagon using either Pythagoras' theorem or trigonometric ratiosI.e., 6\u00b2 + (x/2)\u00b2 = x\u00b2Or Cos 30\u00b0 = 6/xBoth should resolve toX = 4sqrt(3)Anyway, now you can find the area of the triangle and multiply by 6A = 6\u00d7\u00bdbh= 6\u00d7\u00bd\u00d76\u00d74sqrt(3)72\u00d7sqrt(3)124.71 m (2 d.p.)

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