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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Hapa kuna hesabu za eneo lililotiwa kivuli kwa kila mchoro: Mchoro wa Kwanza (Juu kushoto): Mstatili mkubwa wenye mstatili mdogo usio na kivuli ndani yake. Urefu wa mstatili wa nje ni 28 cm na upana ni 20 cm. Urefu wa mstatili wa ndani ni 28 - 2 - 2 = 24 cm na upana ni 20 - 8 - 2 = 10 cm. Step 1: Pata eneo la mstatili wa nje. A_nje = urefu × upana = 28 cm × 20 cm A_nje = 560 cm^2 Step 2: Pata eneo la mstatili wa ndani usio na kivuli. A_ndani = urefu × upana = 24 cm × 10 cm A_ndani = 240 cm^2 Step 3: Kokotoa eneo lililotiwa kivuli. Eneo lililotiwa kivuli = Eneo la mstatili wa nje - Eneo la mstatili wa ndani A_kivuli = 560 cm^2 - 240 cm^2 Eneo lililotiwa kivuli = 320 cm^2 Mchoro wa Pili (Juu kulia): Mraba wenye duara ndani yake. Urefu wa upande wa mraba ni 14 cm. Kipenyo cha duara ni 14 cm, hivyo rediasi ni r = (14)/(2) = 7 cm. Step 1: Pata eneo la mraba. A_mraba = upande^2 = (14 cm)^2 A_mraba = 196 cm^2 Step 2: Pata eneo la duara. (Tumia = (22)/(7)) A_duara = r^2 = (22)/(7) × (7 cm)^2 A_duara = (22)/(7) × 49 cm^2 A_duara = 22 × 7 cm^2 = 154 cm^2 Step 3: Kokotoa eneo lililotiwa kivuli. Eneo lililotiwa kivuli = Eneo la mraba - Eneo la duara A_kivuli = 196 cm^2 - 154 cm^2 Eneo lililotiwa kivuli = 42 cm^2 Mchoro wa Tatu (a) (Katikati kushoto): Umbo la pete (annulus) lenye duara mbili zenye kituo kimoja. Rediasi ya duara kubwa ni R = 14 cm. Rediasi ya duara ndogo ni r = 7 cm. Step 1: Pata eneo la duara kubwa. (Tumia = (22)/(7)) A_kubwa = R^2 = (22)/(7) × (14 cm)^2 A_kubwa = (22)/(7) × 196 cm^2 A_kubwa = 22 × 28 cm^2 = 616 cm^2 Step 2: Pata eneo la duara ndogo. (Tumia = (22)/(7)) A_ndogo = r^2 = (22)/(7) × (7 cm)^2 A_ndogo = (22)/(7) × 49 cm^2 A_ndogo = 22 × 7 cm^2 = 154 cm^2 Step 3: Kokotoa eneo lililotiwa kivuli. Eneo lililotiwa kivuli = Eneo la duara kubwa - Eneo la duara ndogo A_kivuli = 616 cm^2 - 154 cm^2 Eneo lililotiwa kivuli = 462 cm^2 Mchoro wa Nne (Katikati kulia): Mstatili wenye duara ndani yake. Urefu wa mstatili ni 15 cm na upana ni 12 cm. Kipenyo cha duara ni 14 cm, hivyo rediasi ni r = (14)/(2) = 7 cm. Step 1: Pata eneo la mstatili. A_mstatili = urefu × upana = 15 cm × 12 cm A_mstatili = 180 cm^2 Step 2: Pata eneo la duara. (Tumia = (22)/(7)) A_duara = r^2 = (22)/(7) × (7 cm)^2 A_duara = (22)/(7) × 49 cm^2 A_duara = 22 × 7 cm^2 = 154 cm^2 Step 3: Kokotoa eneo lililotiwa kivuli. Eneo lililotiwa kivuli = Eneo la mstatili - Eneo la duara A_kivuli = 180 cm^2 - 154 cm^2 Eneo lililotiwa kivuli = 26 cm^2 Tuma swali linalofuata 📸