Mavzu: Trapetsiya va parallelogrammning yuzi

Ikkala guruhlarga bajarish uchun bittadan masala beriladi:

1-masala. Parallelogrammning bir tomoni 8 sm va perimetri 40 sm ga teng. Agar 8 sm li tomonga tushirilgan balandlik 6 sm bo’lsa, boshqa balandligini toping.
Berilgan:
CD=8 sm S= 8*6=48
P=40 sm AD=(40-16)/2=12
B F=6 sm S=AD*BE
BE=? 48=12*BE
BE=48:12=4
2-masala. Teng yonli uchburchakning asosiga tushirilgan balandli 5 sm, yon tomoni 7 sm va perimetri 22 sm bo’lsa, Uchburchak yuzini toping.

Berilgan:

BD= 5 sm AC=22-(7+7)=8
AB=BC=7 sm S=1/2*8*5=20
P =22 sm S= 20 sm²
S=?
T eorema: Rombning yuzi uning diagonallari ko’paytmasining yarmiga teng.


Isboti: =4*S_AOB S_AOB=1/2*AO*OB
S=4*1/2*AO*OB=1/2*2*AO*2*OB=
=1/2*AC*BD.
Teorema: Trapetsiyaning yuzi uning asoslari yig`indisining yarmi bilan balandligining ko`paytmasiga teng.
F D B C

N



M

h

A a E

AB = a, CD = b, CE = AF = h, CE┴AB;AF┴CD

Isbotlash kerak: S_tr = S_ABCD =
Isboti: Tropetsiyaning diognali AC uni 2 ta uchburchakka ajratadi, uning esa shu uchburchaklarning yuzlari yig`indisiga teng,
S<sub>tr</sub> = S<sub>ABC</sub> + S<sub>ADC</sub> =
Yani: S<sub>tr</sub> =
Bu teoremadan ushbu natijani aniqlash mumkin. Trapetsiyaning yuzi uning o`rta chizig`i bilan balandligining ko`paytmasiga teng.

Yani : S_tr = MN *h =

YANGI MAVZUNI MUSTAHKAMLASH:

24. 1) Berilgan Yechish.

a = 21 sm S_tr =
b = 15 sm J: 90 sm­­²

S_tr - ?

2) Berilgan Yechish.
a = 5 m S_tr =
b = 6 m J: m­­²
a =2.5*b=2.5*6=15sm
S_tr - ?