The apothem

The apothem of a regular hexagon is 5√3 inches. Find one of its sides and area.

Correct answer:

a =  10 in
A =  259.8076 in2

Step-by-step explanation:

h=5 3=5 3 in8.6603 in n=6  Θ=2 n360=2 6360=30   tan  Θ = a/2 : h  a=2 h tanΘ=2 h tan30° =2 8.6603 tan30° =2 8.6603 0.57735=10=10 in
A1=21 a h=21 10 8.6603=25 3 in243.3013 in2  A=n A1=6 43.3013=150 3=259.8076 in2

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