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 hatua za kutafuta eneo la kila umbo: Umbo la Kwanza (Chini): Umbo hili linaweza kugawanywa katika mstatili tatu. Step 1: Tafuta eneo la mstatili wa kwanza (chini). Urefu = 8 sm, Upana = 2 sm. Eneo_1 = urefu × upana = 8 sm × 2 sm = 16 sm^2 Step 2: Tafuta eneo la mstatili wa pili (katikati). Urefu = 6 sm, Upana = 2 sm. Eneo_2 = urefu × upana = 6 sm × 2 sm = 12 sm^2 Step 3: Tafuta eneo la mstatili wa tatu (juu). Urefu = 4 sm, Upana = 2 sm. Eneo_3 = urefu × upana = 4 sm × 2 sm = 8 sm^2 Step 4: Jumlisha maeneo yote kupata eneo kamili la umbo. Eneo Jumla = Eneo_1 + Eneo_2 + Eneo_3 = 16 sm^2 + 12 sm^2 + 8 sm^2 = 36 sm^2 Eneo kamili la umbo la kwanza ni 36 sm^2. Umbo la Pili (Katikati): Umbo hili linaweza kugawanywa katika mraba mmoja wa katikati na mstatili nne zinazouzunguka. Step 1: Tafuta eneo la mraba wa katikati. Urefu = 5 sm, Upana = 5 sm. Eneo_mraba = urefu × upana = 5 sm × 5 sm = 25 sm^2 Step 2: Tafuta eneo la mstatili mmoja wa pembeni. Urefu = 5 sm, Upana = 2 sm. Eneo_mstatili mmoja = urefu × upana = 5 sm × 2 sm = 10 sm^2 Step 3: Tafuta eneo la mstatili zote nne za pembeni. Kuna mstatili nne, hivyo: Eneo_mstatili nne = 4 × 10 sm^2 = 40 sm^2 Step 4: Jumlisha eneo la mraba na eneo la mstatili zote nne. Eneo Jumla = Eneo_mraba + Eneo_mstatili nne = 25 sm^2 + 40 sm^2 = 65 sm^2 Eneo kamili la umbo la pili ni 65 sm^2. Umbo la Tatu (Juu): Umbo hili lina pembetatu na nusu duara. Step 1: Tafuta eneo la pembetatu. Msingi = 10 sm, Kimo = 9 sm. Eneo_pembetatu = (1)/(2) × msingi × kimo = (1)/(2) × 10 sm × 9 sm = 45 sm^2 Step 2: Tafuta eneo la nusu duara. Kipenyo = 10 sm, hivyo rediasi r = 10 sm2 = 5 sm. Eneo_nusu duara = (1)/(2) × × r^2 = (1)/(2) × × (5 sm)^2 = (1)/(2) × × 25 sm^2 = 12.5 sm^2 Kutumia ≈ 3.14159: 12.5 sm^2 ≈ 12.5 × 3.14159 sm^2 ≈ 39.27 sm^2 Step 3: Jumlisha eneo la pembetatu na eneo la nusu duara. Eneo Jumla = Eneo_pembetatu + Eneo_nusu duara = 45 sm^2 + 12.5 sm^2 Eneo Jumla ≈ 45 sm^2 + 39.27 sm^2 = 84.27 sm^2 Eneo kamili la umbo la tatu ni 45 + 12.5 sm^2 ≈ 84.27 sm^2. Tuma swali linalofuata 📸