55.6 cm^2 approx.
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The apothem and side length are not consistent. That is, a nonagon with an apothem of 5.6 cm cannot have a side length of 4.1 cm.If the apothem is 5.6 cm then area = 102.7 cm2 whileif the side length is 4.1 cm then area = 103.9 cm2.The two answers agree at the tens place and so the most accurate answer is 100 cm2 to the nearest 10.
Each side is 117/9 = 13 cm
The area of a regular hexagon with side lengths of 8cm is about 166.3cm2
The area of a nonagon with side L is 6.18182 x L squared. If L = 4, L squared = 16, so area is 98.91 square cm. Now I didn't know the formula, I got it from Wikipedia, so you could do that too.
378 cm ^2