This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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9. Tafuta eneo la msambamba ufuatao: (Pata eneo la trapeza ifuatayo, kwa kudhani ni trapeza pacha (isosceles trapezoid) kwani umbo linaonyesha trapeza na si msambamba (parallelogram) kama ilivyoelezwa.) Hatua ya 1: Tambua vipimo vya trapeza. Trapeza ina urefu wa msingi wa juu a = 24 Sm na msingi wa chini b = 42 Sm. Upande mmoja mteremko ni c = 30 Sm. Kwa trapeza pacha, tofauti ya nusu ya misingi inatoa urefu wa sehemu ya msingi wa chini inayounda pembetatu ya kulia na urefu h. x = (b - a)/(2) = 42 Sm - 24 Sm2 = 18 Sm2 = 9 Sm Hatua ya 2: Tafuta urefu (h) wa trapeza kwa kutumia kanuni ya Pythagoras. Katika pembetatu ya kulia, x ni upande mmoja, h ni upande mwingine, na c ni hipotenusi. h^2 + x^2 = c^2 h^2 + (9 Sm)^2 = (30 Sm)^2 h^2 + 81 Sm^2 = 900 Sm^2 h^2 = 900 Sm^2 - 81 Sm^2 h^2 = 819 Sm^2 h = sqrt(819) Sm Hatua ya 3: Kokotoa eneo la trapeza. Eneo la trapeza hutolewa na fomula: A = (1)/(2)(a+b)h. A = (1)/(2)(24 Sm + 42 Sm)sqrt(819) Sm A = (1)/(2)(66 Sm)sqrt(819) Sm A = 33 sqrt(819) Sm^2 A ≈ 33 × 28.618 Sm^2 A ≈ 944.39 Sm^2 Eneo la trapeza ni: 944.39 Sm^2 10. Tafuta eneo la mcheduara ufuatao iwapo umefungwa upande mmoja. (Tumia = 22/7) (Pata eneo la umbo lifuatalo. Umbo hili lina mstatili katikati na nusu-duara mbili kwenye ncha zake.) Hatua ya 1: Tambua vipimo vya umbo. Urefu jumla wa umbo ni 100 Sm. Kipenyo cha nusu-duara ni 14 Sm. Hivyo, rediasi ya nusu-duara ni r = 14 Sm2 = 7 Sm. Hatua ya 2: Kokotoa vipimo vya mstatili. Upana wa mstatili ni sawa na kipenyo cha duara, yaani 14 Sm. Urefu wa mstatili ni urefu jumla ukiondoa rediasi mbili (moja kila upande): Urefu wa mstatili = 100 Sm - (7 Sm + 7 Sm) = 100 Sm - 14 Sm = 86 Sm. Hatua ya 3: Kokotoa eneo la mstatili. Eneo la mstatili = urefu × upana A_mstatili = 86 Sm × 14 Sm = 1204 Sm^2 Hatua ya 4: Kokotoa eneo la duara kamili (kutoka nusu-duara mbili). Nusu-duara mbili huunda duara kamili. Eneo la duara = r^2 A_duara = (22)/(7) × (7 Sm)^2 A_duara = (22)/(7) × 49 Sm^2 A_duara = 22 × 7 Sm^2 = 154 Sm^2 Hatua ya 5: Kokotoa eneo jumla la umbo. Eneo jumla = Eneo la mstatili + Eneo la duara A_jumla = 1204 Sm^2 + 154 Sm^2 = 1358 Sm^2 Eneo la umbo ni: 1358 Sm^2 Tuma swali linalofuata 📸