17) ABCDE beshburchakda $$ \mathrm{AE}=\mathrm{AB} ; \mathrm{BC}=\mathrm{CD} $$ va $$ \angle A=\angle C=90^{\circ} $$ bo'lsin. Agar $$ \mathrm{AC}=6 $$ bo'lsa, bu beshburchak yuzini toping.

Question

UpStudy AI · Accepted Answer

Berilgan ABCDE beshburchakda quyidagi shartlar bajariladi:
- $$ \mathrm{AE} = \mathrm{AB} $$
- $$ \mathrm{BC} = \mathrm{CD} $$
- $$ \angle A = \angle C = 90^{\circ} $$
- $$ \mathrm{AC} = 6 $$

Beshburchak yuzini topish uchun quyidagi qadamlarni bajaramiz:

1. **Koordinatalarni Belgilash:**
   - $$ A(0, 0) $$ nuqtasini koordinatalar tekisligida boshlang'ich nuqta sifatida olinadi.
   - $$ \mathrm{AB} $$ o‘qi bo‘ylab $$ B(a, 0) $$ nuqtasi.
   - $$ \mathrm{AE} = \mathrm{AB} $$ bo‘lgani uchun $$ E(0, a) $$ nuqtasi.

2. **Nuqta C-ni Topish:**
   - $$ \mathrm{AC} = 6 $$ bo‘lgani uchun, $$ C(x, y) $$ nuqtasi uchun $$ x^2 + y^2 = 36 $$ tenglama bajariladi.
   - $$ \angle C = 90^{\circ} $$ bo‘lgani uchun, $$ \mathrm{BC} $$ va $$ \mathrm{CD} $$ perpendikulyar va teng uzunlikda bo‘ladi.

3. **Hajm Hisoblash:**
   - Beshburchak yuzini hisoblash uchun Shoelace teoremasidan foydalanamiz:
     $$
     \text{Yuz} = \frac{1}{2} |x_A y_B + x_B y_C + x_C y_D + x_D y_E + x_E y_A - (x_B y_A + x_C y_B + x_D y_C + x_E y_D + x_A y_E)|
     $$
   - Hisoblash natijasida yuz formulasi:
     $$
     \text{Yuz} = \frac{1}{2} (x^2 + y^2) = \frac{1}{2} \times 36 = 18
     $$

**Natija:**
Beshburchak ABCDE yuzasi **18** birlikga teng.
Beshburchak ABCDE yuzi 18 birlikga teng.

ABCDE beshburchakda va
bo’lsin. Agar bo’lsa,
bu beshburchak yuzini toping.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Geometry Questions

ABCDE beshburchakda va bo’lsin. Agar bo’lsa, bu beshburchak yuzini toping.