Mundarija: Kirish I bob. Ko’pburchaklarni o’qitish

FORMULALAR

Qavariq ko’pburchak ichki burchaklarining yig’indisi:

(n-2)180 0 ga teng

Qavariq ko’pburchak tashqi burchaklarining yig’indisi:

360 0 ga teng

Qavariq ko’pburchak diagonallari soni:

(n  3)n _{ga teng}

2

S _n = ¹₂ P_n  r


¹⁸⁰⁰
ar  2R sin


_{S n =} ¹ _R 2 _sin ³⁶⁰⁰

2 n

Masalalarning yechilishi

1. 
   Qavariq ko’pburchak ichki burchaklari yig’indisi (n-2)180 0 ga teng. n=5 bo’lganda
   

  (5  2)180⁰ =3 180⁰ =540 ⁰ javob: 540 ⁰

2. Berilgan:


^P1 _²


P₂ 3

S₂=27

S₁=?
3. Berilgan:

• 
  135⁰
  

n=?

4. Berilgan:

• 
  120⁰
  

n=?

	S	1		P	^2
YECHISH:				1		ekanligidan foydalanib,
	^S 2		^	^P2	
					

19. 
    _2²
    
    1. 
       
       

27 3

	S1			4		 9S1=4 27
27				9
S 1 =			427				 4  3 12javob: 12
				9

YECHISH:   ^{(n  2)1800}


n

135	^0 =	(n  2)180	0	bundan,
		n

135 ⁰ n  (n  2)180⁰

135 ⁰ n 180⁰ n  2 180⁰

135 ⁰ n 180⁰ n  360⁰

180 ⁰ n 135⁰ n  360⁰

45 ⁰ n  360⁰

n 	360^0		 8 javob: 8.
45^0
YECHISH: 120 0 				(n  2)180^0
				n
120 ^0 n  (n  2)180^0

120 ⁰ n 180⁰ n  360⁰

180 ⁰ n 120⁰ n  360⁰

60 ⁰ n  360⁰

n 	360^0	 6	n=6 javob: 6.
	60^0

5. Ichki burchaklari yig’indisi: (n-2)180 0

bitta ichki burchagi:  							(n  2)180^0	, n=8 bo’lgani uchun
							n
	(8  2)180^0			6 180	0	135^0135^0
	8			8
   180^0			  tashqi burchak
 180^0 135^0				bundan   45^0				javob: 45 0

6. 
     240 ko’pburchakning tashqi burchaklari yig’indisi n  3600 bundan 24 0 n=360 0
   

n=	360^0	15 n=15 javob: 15.
	24^0
7.Qavariq ko’pburchakning diagonallari soni:			(n  3)n		 90
			2

n ² 3n 180

n²  3n 180  0 bunda n>0

D=9+4 180  729

^n 1,2



3 

D

bundan,

2

3 

327

n=

729



15

javob: 15 ta.

2

2

8. Berilgan:

YECHISH: an

 a1  (n 1)d

a2  a1  4

d= a2  a1  4

a

 23

S



a1  an

n

a  a

 (n 1)d

n

n

n

2

1

S n  P  75

75=

an  (n 1)d  an

n

2

n=?

150= (2 an  (n 1)d )n

150=(2 23 -4(n-1))n

150=(46-4n+4)n

150=50n-4n 2

4n 2 -50n+150=0 bundan n=5 javob: 5

II-bob. Ko’pyoqlar va ularni o’qitish metodikasi.