Divide the nonagon radially into 9 congruent, equilateral isosceles triangle. Each triangle has vertex angle of 360°/9 = 40°.
Interior angle of polygon = 180°-40° = 140°.
Sum of interior angles = 9(140°) = 1260°
Answer:




Step-by-step explanation:
Given
See attachment
From the attachment, we have:


First, we need to calculate length LM,
Using Pythagoras theorem:



Collect Like Terms



Solving (a): 


Substitute values for MN and LN


Solving (b): 


Substitute values for LM and MN


Solving (c): 


Substitute values for LN and LM


Solving (d): 


Substitute values for LM and LN


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75.3982237 inches squared is the answer, round it to whatever decimal place your asked to.