42. $$ A B C D $$ trapetsiyaning asoslari 4 va 25 , yon tomonlari 13 va 20 ga teng. Bunga ko'ra $$ a $$ va $$ b $$ shartlarni bajaring. Shartlarni bajarishda $$ \pi \approx 3 $$ deb hisoblansin. a) Trapetsiya yuzini toping. $$ \quad $$ [1,5 ball] Javob: a) b) Trapetsiyani kichik asos atrofida $$ \mathbf{3 6 0}^{\circ} $$ ga aylantirishdan hosil bo'lgan jism hajmini toping. Javob: b) Diqqat! Javoblaringizni javoblar varaqasiga ko'chirib yozing.

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### a) Trapetsiya yuzi

Trapetsiyaning yuzini topish uchun quyidagi formula ishlatiladi:

$$
S = \frac{(a + b)}{2} \times h
$$

Bu yerda:
- $$ a = 4 $$ (kichik asos)
- $$ b = 25 $$ (katta asos)
- $$ h = 12 $$ (balandlik)

$$
S = \frac{(4 + 25)}{2} \times 12 = \frac{29}{2} \times 12 = 174
$$

**Javob: a) 174**

### b) Trapetsiyani kichik asos atrofida aylantirishdan hosil bo'lgan jism hajmi

Trapetsiyani kichik asos atrofida $$360^\circ$$ aylantirishdan hosil bo'ladigan hajm $$V$$ quyidagi formula orqali hisoblanadi:

$$
V = 2 \pi \times d \times S
$$

Bu yerda:
- $$ \pi \approx 3 $$
- $$ S = 174 $$ (trapetsiyaning yuzi)
- Centroid masofasi $$ d = \frac{216}{29} $$ deb topilgan

$$ 
V = 2 \times 3 \times \frac{216}{29} \times 174 = 7776
$$

**Javob: b) 7776**
a) Trapetsiya yuzi 174. b) Trapetsiyani aylantirishdan hosil bo'lgan jism hajmi 7776.

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