I. Burchaklar. Masofalar

7. Uchburchak medianasining xossalari.
1. Uchburchakning asosi 22 ga, yon tomonlari 13 va 19 ga teng. Asosiga tushirilgan medianasini toping.
A) 18 B) 12 C) 16 D) 13 Ye) 14
2. Uchburchakning tomonlari 11 va 23 ga. uchinchi tomoniga tushirilgan medianasi 10 ga teng. Uchburchakning uchinchi tomonini toping.
A) 30 B) 15 C) 25 D) 28 Ye) 26
3. Uchburchakning tomonlari 7 va 11 ga, uchinchi tomonining medianasi 6 ga teng. Uchburchakning uchinchi tomonini toping.
A) 12 B) 14 C) 15 D) 16 E) 18
4. Uchburchakda medianalar kvadratlarining yig‘indisini tomonlari kvadratlari yig‘indisiga nisbati nechaga teng?
A) B) C) D) E)
5. Uchburchak tomonlari 7 va 11 ga, uchinchi tomoniga tushirilgan medianasi 6 ga teng. Uchburchakning uchinchi tomonini toping.
A) 12 B) 8 C) 14 D) 10 E) 13
6. AVS uchburchakning AK medianasi AS tomon bilan 30º burchak tashkil qiladi. Agar AK = va bo‘lsa, VS tomonning uzunligini toping.
A) B) C) 5,5 D) E) 6,5
9. Uchburchakning yuzi.
1. To‘g‘ri burchakli uchburchak kateti 8 sm, uning gipotenuzadagi proeksiyasi esa 6,4 sm. Shu uchburchakning yuzasi necha sm² ?
A) 25,6 B) 48 C) 51,2 D) 24 E) 18
2. Uchburchakning a va b tomonlari orasidagi burchak α ga teng. Uchburchak yuzasi quyidagi ifodalardan qaysi biriga teng?
A) ab · sinα B) C) D) 2ab · cosα E)
3. ABC uchburchakda AB=5 sm, AC=10 sm va A=45. Shu uchburchakning yuzi necha sm².
A) B) 10 C) 50 D) 25 E) 25
4. Tomonining uzunligi bo‘lgan muntazam uchburchakning yuzini toping.
A) 12 B) 16 C) 24 D) 12 E) 8
5. Tomonlari 13; 14 va 15 sm bo‘lgan uchburchakning eng kchik balandligi necha sm?
A) 11,2 B) 11,1 C) 11 D) 11,5 E) 11,6
6. To‘g‘ri burchakli uchburchakning katetlaridan biri 12, gipotenuzasi esa ikkinchi katetdan 6 ga ortiq. Uchburchakning yuzini toping.
A) 36 B) 40 C) 42 D) 54 E) 60
7. To‘g‘ri burchakli uchburchak gipotenuzasi 50 sm, katta katetning gipotenuzadagi
proeksiyasi 32 sm. Shu uchburchak yuzini toping.
A) 1200 B) 576 C) 300 D)600 E) 800
8. To‘g‘ri burchakli uchburchak gipotenuzasi 10 sm, kichik katetning gipotenuzaga proeksiyasi esa 3,6 sm. Shu uchburchakning yuzi necha sm² ?
A) 48 B) 24 C) 18 D) 32 E) 20,4
9. AVS uchburchakda AV sm, AS sm va A 45. Shu uchburchakning yuzi necha sm?
A) B) C) D) E)
10. AVS uchburchakda AV = 3 sm, AS = 6 sm va A = 45º. Shu uchburchakning yuzi
necha sm²?
A) B) C) D) E)
12. Katetlarining nisbati 2:3 kabi bo‘lgan to‘g‘ri burchakli uchburchakning gipotenuzasi 13 ga teng. Uchburchakning yuzini toping.
A) B) 24 C) 39 D) 36 Ye)
13. Agar uchburchakning asosi 20% uzaytirilib, balandligi 20% qichqartirilsa, uning yuzi qanday o‘zgaradi?
A) o‘zgarmaydi B) 4% kamayadi C) 4% ortadi D) 6% kamayadi E) 6% ortadi
14. Katetlaridan biri 8 ga teng bo‘lgan to‘g‘ri burchakli uchburchak gipotenuzasining ikkinchi katetiga nisbati 5:3 ga teng. Uchburchakning yuzini toping.
A) 12 B) 15 C) 20 D) 24 Ye) 48
15. Uchburchakning katetlaridan biri 6 ga teng, ikkinchisi gipotenuzadan 2 ga kam. Uchburchakning yuzini toping.
A) 24 B) 18 C) 15 D) 12 E) 30
16. Uchburchakning yuzi 6 ga teng. Shu uchburchakning 3 va 8 ga teng tomonlari orasidagi burchakni toping.
A) 30° B) 45° C) 60° D) 60° yoki 120° Ye) 30° yoki 150°
17. Teng yonli uchburchakning perimetri 14 ga teng. Asosi yon tomonidan 3 marta kichik. Uchburchakning yuzini toping.
A) 4 B) 8 C) D) 12 Ye) 2
18. Muntazam uchburchakning yuzi 25 ga teng. Uning tomonini toping.
A) 15 B) 20 C) 10 D) 12 Ye) 8
19. ABC uchburchakda A=30º, AB= , AC=4. A uchidan tushirilgan balandlik uzunligini toping.
A) B) C) D) E)
20. Muntazam uchburchakning ichidagi ixtiyoriy nuqtadan uning tomonlarigacha bo‘lgan masofalar yig‘indisi ga teng. Uchburchakning yuzini toping.
A) 4 B) 3 C) D) E) aniqlab bo‘lmaydi.
21. funksiyaning OX o‘qi bilan kesishish nuqtalaridan hamda funksiya grafigining eng quyi nuqtasini tutashtirishdan hosil bo‘lgan uchburchakning yuzini hisoblang.
A) B) C) D) E)
22. 2x + 3y – 6 = 0 to‘g‘ri chiziq va koordinata o‘qlari bilan chegaralangan uchburchakning yuzini toping.
A) 3 B) 4 C) 2 D) 6 Ye) 1
23. Teng yonli uchburchakning asosi 18 ga, yuzi 108 ga teng. Shu uchburchakning yon tomonini toping.
A) 15 B) 16 C) 12,5 D) 21 Ye) 25
24. parabolaning grafigi OX o‘qini A va B nuqtalarda, OY o‘qini S nuqtada kesib o‘tadi. ABC ning yuzini toping.
A) 8 B) 12 C) 10 D) 6 E) 9
25. AVS ning AV va VS tomonlari orasidagi burchagi 30° ga teng. Agar AV va VS tomonlar orasidagi burchak 120° ga orttirilsa, AVS ning yuzi qanday o‘zgaradi?
A) 4 marta ortadi B) 4 marta kamayadi C) o‘zgarmaydi D) marta ortadi Ye) marta kamayadi
26. ABC uchburchkda A=30º, AB= , AC=6. A uchidan tushirilgan balandlikning uzunligini toping.
A) B) C) D) E)
27. Agar teng yonli to‘g‘ri burchakli uchburchakning yuzasi 18 ga teng bo‘lsa, gipotenuzaning uzunligi qanchaga teng bo‘ladi?
A) 6 B) C) 2 D) E)
28. y = –x –1, y = x – 1 to‘g‘ri chiziqlar va OX o‘qi bilan chegaralangan figuraning yuzini toping.
A) 2 B) 1 C) D) E)
29. Ikki tomonining yig‘indisi 4 ga va ular orasidagi burchagi 120º ga teng bo‘lgan uchburchakning yuzi eng ko‘pi bilan nechaga teng bo‘lishi mumkin?
A) B) 2 C) D) 1 E)
31. AVS uchburchakning AV va AS
tomonlarida shunday K va N nuqtalar olindiki, ga va ga teng bo‘ldi. AVS uchburchakning yuzi 18 ga teng. AKN uchburchakning yuzini toping.
A) 4 B) 6 C) 9 D) 2 E) 3
32. Uchburchakning ikki tomoni uzunliklari 6 va 3 ga teng. Agar bu tomonlarga o‘tkazilgan balandliklar uzunliklari yig‘indisining yarmi uchinchi tomonga o‘tkazilgan balandlikka teng bo‘lsa, uchinchi tomon uzunligini aniqlang.
A) 6 V) 5 S) 3 D) 4 E) 7
33. To‘g‘ri burchakli uchburchak katetlarining gipotenuzadagi proeksiyalari 8 va 2 ga teng. Uchburchakning yuzini toping.
A) 10 V) 20 S) 40 D) 24 Ye) 16
34. 3x + u + 12 = 0 to‘g‘ri chiziq va koordinata o‘qlari bilan chegaralangan uchburchakning yuzini aniqlang.
A) 64 V) 12 S) 48 D) 36 Ye) 24
35. Shaklga ko‘ra va bo‘lsa, yuzining yuziga nisbatini hisoblang.

A) 4: 1 V) 6:1 S) 3:2 D) 10 :3 Ye) 9 : 4
36. ABC uchburchakning AD medianasi 6 ga, AC tomoni 8 ga va ular orasidagi burchak 30º ga teng. ABC uchburchakning yuzini toping.
A) 28 B) 26 C) 22 D) 30 E) 24
37. AVS uchburchakning AV, VS va SA tomonlarida olingan M, N va R nuqtalar shu tomonlarni 1 : 2 nisbatda bo‘ladi. Agar AVS uchburchakkikg yuzi S ga teng bo‘lsa, MNP uchburchakning yuzini toping.
A) B) C) D) E)
38. Muntazam uchburchakning yuzi 64 ga teng. Uning perimetrini toping.
A) B) C) 64 D) E)
39. To‘g‘ri burchakli uchburchakning katetlari 4 va 6 ga teng. Shu uchburchakning to‘g‘ri burchagidan chiqarilgan bissektrisasining uzunligini toping.
A) 3,6 V) S) D) 4,8 Ye)
40. Teng yonli to‘g‘ri burchakli uchburchakning yuzi 1225 ga teng bo‘lsa, uning gipotenuzasini toping.
A) 70 B) 65 C) 72 D) 49 E) 50
41. AVS uchburchakning BD, AE va CF medianalari O nuqtada kesishadi. AOD ning yuzi 2,8 ga teng. BFC ning yuzini toping.
A) B) C) D) E)
42. Teng yonli to‘g‘ri burchakli uchburchakning gipotenuzasi ga teng. Uning yuzini hisoblang.
A) 14,5 B) 12,5 C) 10,5 D) 8,5 E) 16,5
43. Gipotenuzasi s ga va o‘tkir burchaklari sinuslarining yig‘indisi q ga teng bo‘lgan to‘g‘ri burchakli uchburchakning yuzini toping.
A) B) C) D) E)
44. Uchburchakning ikkita tomoni 3 va 7 ga, ular orasidagi burchak 120° ga teng. Uchburchakning shu burchagi uchidan chiqqan bissektrisasini toping.
A) 1,7 V) 1,8 S) 1,9 D) 2,1 Ye) 2,3
45. Yuzi 48 ga teng bo‘lgan AVS uchburchakning AS tomoni D nuqtada AD : DC= 1:7 kabi nisbatda bo‘linadi. AVD uchburchakning yuzini aniqlang.
A) 4 B) 6 C) 5,5 D) 8 E) 12
46. Uchburchakning ichidagi M nuqtadan uning tomonlariga parallel to‘g‘ri chiziqlar o‘tkazildi. Natijada berilgan uchburchakning kchida M nuqtada umumiy uchga ega, yuzalari esa 3; 12 va 27 ga teng bo‘lgan uchta uchburchak hosil bo‘ldi. Berilgan uchburchakning yuzini toping.
A) 84 V) 72 S) 108 D) 144 Ye) 96
47. AVS uchburchakda S = 135º, AC = 6 va BD balandlik 2 ga teng. ABD uchburchakning yuzini toping.
A) 8 B) 6 C) 16 D) 12 E) 10
48. y + x = 0, y  x + 6 = 0 to‘g‘ri chiziqlar va Ox o‘qi bilan chegaralangan uchburchakning yuzini toping.
A) 9 B) 18 C) 4,5 D) 12 E) 16
49. Yon tomoni a ga teng bo‘lgan teng yonli uchburchakning asosi qanday bo‘lganda uning yuzi eng katta bo‘ladi?
A) 2a B) C) D) E) 2001-7-50
50. To‘g‘ri burchali uchburchakning katetlari log₄9 va log₃16 ga teng. Uning yuzini toping.
A) 3 B) 4 C) 5 D) 10 E) 2
51. AVS uchburchakda medianalar kesishgan nuqtadan AV tomongacha bo‘lgan masofa 1 ga teng. Agar AV = 8 bo‘lsa, AVS uchburchakning yuzini toping.
A) 12 B) 16 C) 9 D) 13 E) 10
53. To‘g‘ri burchakli uchburchakning perimetri 84 ga, gipotenuzasi 37 ga teng. Bu uchburchakning yuzini toping.
A) 210 V) 240 S) 105 V) 420 Ye) 180
54. Uchburchakning ikki tomoni va ular orasidagi bissektrisasi uzunligi mos ravishda 60; 40 va 24 ga teng. Uchburchak yuzini toping.
A) 600 V) 800 S) 400 D) 300 E) 900
55. AVS uchburchakning yuzi 12 ga teng. Uning V uchidan BD = 3 mediana tushirilgan. Agar ABD = 90° bo‘lsa, AS tomonning uzunligini toping.
A) 2 V) S) 8 D) 10 Ye) 12
56. Uchburchakning yuzi 5 ga, ikkita tomoni 3 va 4 ga teng. Berilgan tomonlar orasidagi burchak bissektrisasi ajratgan uchburchaklarning yuzlarini toping.
A) B) C) 2; 3 D) E)
57. To‘g‘ri burchakli ASV uchburchakning katetlari 8 ga va 10 ga teng. Shu uchburchakning S to‘g‘ri burchagi uchidan SE mediana va CD bissektrisa o‘tkazildi. CDE uchburchakning yuzini toping.
A) 2 B) 2 C) D) E)
58. Teng yonli uchburchakning yon tomoni 2 ga teng. Shu uchburchakning yuzi eng katta bo‘lishi uchun, asosi nimaga teng bo‘lishi kerak?
A) B) C) D) E) 1,5
59. Asosi a va unga yopishgan burchaklari 30° va 45° bo‘lgan uchburchakning yuzini
toping.
A) B) C) D) E)
60. Asosi a va unga tushirilgan balandligi h ga teng bo‘lgan uchburchak ichiga parallelogramm shunday chizilganki, parallelogrammning bir tomoni a asosda yotadi. Shu parallelogrammning yuzi eng katta qiymatga ega bo‘lishi uchun uning asosini qanday tanlab olish kerak?
A) B) C) D) E)