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If you have the side length S, the formula is
1/4 sqrt [(25 +10 (sqrt5)] S2

which is approximately
1.720477 S2
where
1.72 S2 will be a good estimate

(see related link where side is not given)
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This was derived from the tangential formula A = (5/4) · s2 · tan(3π/10)

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Where only the side (S) is known, I use 5S2/4 tan36.

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Q: What is the formula to find the area of a regular pentagon?
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