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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Ili kutatua swali hili, tutachukulia kuwa umbo lililopewa ni sekta ya duara. Pia, tutachukulia kuwa '500' iliyoandikwa kwenye picha inamaanisha pembe ya 50^ iliyoondolewa kutoka kwenye duara kamili, kwani 500^ haingewezekana kwa muktadha huu. Step 1: Tambua vipimo vilivyopewa na kokotoa pembe ya sekta iliyobaki. Radius ya duara r = 7 m. Pembe ya sehemu iliyoondolewa _removed = 50^. Pembe ya sekta iliyobaki _remaining = 360^ - _removed. _remaining = 360^ - 50^ = 310^ Step 2: Kokotoa eneo la umbo (sekta iliyobaki). Fomula ya eneo la sekta ni A = ()/(360^) × r^2. A = (310^)/(360^) × (7 m)^2 A = (31)/(36) × 49 m^2 A = (1519)/(36) m^2 Kutumia ≈ 3.14159: A ≈ (1519)/(36) × 3.14159 A ≈ 132.59 m^2 Eneo la umbo ni 132.59 m^2. Step 3: Kokotoa urefu wa upinde (arc length) wa sekta iliyobaki. Fomula ya urefu wa upinde ni L = ()/(360^) × 2 r. L = (310^)/(360^) × 2 (7 m) L = (31)/(36) × 14 m L = (217)/(18) m Kutumia ≈ 3.14159: L ≈ (217)/(18) × 3.14159 L ≈ 37.87 m Step 4: Kokotoa perimita (circumference) ya umbo. Perimita ya umbo ni jumla ya urefu wa upinde na radii mbili za moja kwa moja. Perimita P = Urefu wa Upinde + r + r P = (217)/(18) m + 7 m + 7 m P = (217)/(18) m + 14 m P ≈ 37.87 m + 14 m P ≈ 51.87 m Perimita ya umbo ni 51.87 m. 3 done, 2 left today. You're making progress.