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49-rasm.
S=AB*AD sin =24, 5*6sin =24, sin =4/5 cos =3/5
Kosinuslar teoremasiga ko’ra: BD2=25+36-60cos =61-60*3/5=25
BD=5.
9-misol: Agar rombning tomoni 10 ga, burchaklaridan biri esa 1500ga teng bo’lsa, uning yuzi qanchaga teng bo’ladi?
Yechish:

S=absin =10*10sin300=100*1/2=50

300


.
1500

50-rasm
10-misol: To’g’ri to’rtburchakning to’g’ri burchagi uchidan uning diogonaliga tushirilgan perpendikulyar to’g’ri burchakni 3:1 kabi nisbatda bo’ladi. Shu perpendikulyar bilan boshqa diogonali orasidagi burchakni toping.
Yechish. 4x=900, x=22,50, ADB=90-x=67,50.
DBC+ OCB=2 OBC=2*67,50=1350.
BOC=1800-(1350)=450 OAA1=450.

B C



O


A1
3x
x
A D
51-rasm.
11-misol: Diogonallari 6 va 8 ga, ular orasidagi burchak 600 ga teng bo’lgan parallelogrammning perimetrini toping.
Y echish:
B y C
x

A D
52-rasm.


AC=8, BD=6, COD=600

12-misol: Trapetsiyaning asoslari 2 va 3 ga, katta asosiga yopishgan burchaklari 300 va 450 ga teng bo’lsa, trapetsiyaning yuzi qanchaga teng bo’ladi?


Yechish: B C

h h
A D


53-rasm.

BC=2, AD=3, A=300, D=450.




13-misol: ABCD to’g’ri to’rtburchakda AD=12, CD=5, O – diogonallarning kesishish nuqtasi. ni toping.


Yechish:
B C

O


5

A 12 D


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