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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Kutokana na picha, tuna mraba wenye duara ndani yake. Upande wa mraba ni 7 cm. Tutapata eneo la mraba, eneo la duara, na eneo la sehemu iliyobaki ya mraba nje ya duara. Step 1: Tambua vipimo vilivyotolewa. Upande wa mraba (s) ni 7 cm. Kwa duara iliyo ndani ya mraba, kipenyo (d) cha duara ni sawa na upande wa mraba. Hivyo, d = 7 cm. Radiasi (r) ya duara ni nusu ya kipenyo. r = (d)/(2) = 7 cm2 = 3.5 cm Step 2: Kokotoa eneo la mraba. Eneo la mraba (A_mraba) linapatikana kwa fomula s^2. A_mraba = s^2 A_mraba = (7 cm)^2 A_mraba = 49 cm^2 Eneo la mraba ni 49 cm^2. Step 3: Kokotoa eneo la duara. Eneo la duara (A_duara) linapatikana kwa fomula r^2. Tutatumia ≈ 3.14159. A_duara = r^2 A_duara = (3.5 cm)^2 A_duara = (12.25 cm^2) A_duara ≈ 3.14159 × 12.25 cm^2 A_duara ≈ 38.484575 cm^2 Eneo la duara, likizungushwa hadi sehemu mbili za desimali, ni 38.48 cm^2. Step 4: Kokotoa eneo la sehemu ya mraba iliyo nje ya duara. Hili linapatikana kwa kutoa eneo la duara kutoka eneo la mraba. A_iliyobaki = A_mraba - A_duara A_iliyobaki = 49 cm^2 - 38.484575 cm^2 A_iliyobaki ≈ 10.515425 cm^2 Eneo la sehemu iliyobaki, likizungushwa hadi sehemu mbili za desimali, ni 10.52 cm^2. Tuma swali linalofuata 📸