Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side of the regular nonagon be 1 unit.
Therefore;
Area nonagon is;
½(9)*(1/(2tan(180/9)))
= ¼(9)*(1/tan(20))
= 6.18182419377 square units.
Calculating r, radius of the inscribed circle.
2(½(r) + ½(r)√(2-2cos140)) = 2(½(√(2-2cos140))cos120)
r + √(2-2cos140)r = √(2-2cos140)cos120
r = √(2-2cos140)cos120 ÷ (1+√(2-2cos140))
r = 0.56525793742 unit.
Area of the inscribed circle is;
π(0.56525793742)²
= 1.00379080162 square units.
It implies;
Area Circle ÷ Area Nonagon to 2 decimal places is;
= 1.00379080162 ÷ 6.18182419377
= 0.16237776588
≈ 0.16
