Основано на упр. 69, стр. 34
Выполни задание

Найди площадь \(S\) правильного \(n\) -угольника, если:

1. n =
   \(4\) , \(R =\) \(3 \sqrt{2} \) см;

2. n =
   \(3\) , \(P =\) \(24 \) см;

3. n =
   \(6\) , \(r =\) \(9 см\) ;

4. n =
   \(8\) , \(r =\) \(5 \sqrt{3} \) см.

\(n =\) \(4\) , \(a\_4 = R \cdotp \) [ ] \(=\) [ ] \(\cdotp\) [ ] \(=\) [ ] (см)

\(r = R \cdot \cos\) [ ] \(=\) [ ] \(\cdot\) [ ] \(=\) [ ] (см),

S = \(\dfrac{1}{2} P \cdotp \) \(=\) \(\dfrac{1}{2} \cdotp \) [ ] \(\cdotp\) [ ] \(\cdotp\) [ ] \(=\) [ ] \((см^{2})\)

2.

n = 3, \(a\_3\) \(=\) [ ] (см)

                R =                     \(a\_3 : 2 \sin\) [ ] \(=\) [ ] \(:\) [ ] \(=\) [ ]

\(r = R \cdot \cos =\) , \(S =\) \(\dfrac{1}{2} Pr\) \(=\) [ ] \(\cdotp\) [ ] \(=\) [ ] \(см^{2}\) [ ]

3.

\(n = 6, r = R · cos\) [ ] \(=\) [ ] \(\cdot\) [ ], поэтому \(R =\) [ ]

\(a\_6\) \(=\) [ ] \(=\) [ ] см

\(S =\) \(\dfrac{1}{2} \cdot\) [ ] \(\cdot\) [ ] \(\cdot\) [ ] \(=\) [ ]

4.

\(n = 8, r = R · \cos\) [ ]

\(a = 2R · \sin\) [ ] \(= 2r \cdot\) [ ] \(=\) [ ] (см)

\(S =\) \(\dfrac{1}{2}\) \(\cdot 8 \cdot\) [ ] \(=\) [ ] \(\approx\) [ ]

Ответ.

1)[ ]

2)[ ]

3)[ ]

4)[ ]