if P = 24v3, then each side = 4v3

an apothem will bisect a side = 2v3

This bisection will form a 30-60-90 degree right triangle, where the apothem corresponds to xv3 and x corresponds to 2v3

Thus the height of your apothem equals 2v3*v3 = 2 * 3 = 6

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