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Cubic Yards Of Concrete Needed To Pour An Octagon With 6 Foot Sides 15 Inches Thick?

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The area of a regular octagon is given by  area = 2(1+√2)t^2
where t is the length of a side.
The area of your patio is 2(1+√2)(36 ft^2) ≈101.823376 ft^2. If you multiply that by (15/12) ft and divide by 27 ft^3/yd^3, you will have the required number of cubic yards. That amount is ...

(72 * (1 sqrt(2)) * (15 / 12)) / 27 = 4.71404521 yd^3

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