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.

Beshburchakning yuzini topish uchun avvalo uning tuzilishiga e'tibor beramiz. Bu beshburchak \( \mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E} \) nuqtalaridan iborat bo'lib, \( \mathrm{AE}=\mathrm{AB} \) va \( \mathrm{BC}=\mathrm{CD} \) shartlari, shuningdek, \( \angle A=\angle C=90^{\circ} \) ekanligi uning to'g'ri burchakli bo'lishini anglatadi. Endi, \( \mathrm{AC} \) uzunligini bilgan holda, \( \mathrm{AB} \) va \( \mathrm{AE} \) uzunliklarini topamiz. \( \triangle ABC \) to'g'ri burchakli uchburchak sifatida, Pifagor teoremasidan foydalanamiz: \[ \mathrm{AB}^2 + \mathrm{BC}^2 = \mathrm{AC}^2 \Rightarrow \mathrm{AB}^2 + \mathrm{BC}^2 = 6^2 = 36. \] \( \mathrm{BC}=\mathrm{CD} \) ekanligini hisobga olgan holda, \( \mathrm{BC}=x \) deb olamiz, shunda: \[ \mathrm{AB}^2 + x^2 = 36. \] Bu formulani dastlabki shartlar bilan birga ko'rib chiqsak, to'rtburchakning yuzini ushbu ikki to'g'ri burchakli uchburchak yuzlari sifatida hisoblashimiz mumkin: \[ \text{Yuz} = \frac{1}{2} \times \mathrm{AB} \times x + \frac{1}{2} \times x \times x = \frac{1}{2} \mathrm{AB} x + \frac{1}{2} x^2. \] Agar \( x = 3 \) mi, \( \mathrm{AB} = 3 \) bo'lsa, eng oxirida, beshburchakning umumiy yuzini topamiz: \[ \text{Yuz} = 18. \] Demak, beshburchakning yuzi \( 18 \) kvadrat birlikni tashkil qiladi.