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 kukokotoa eneo la umbo zima, tutaligawanya katika maumbo rahisi: mraba mmoja, mistatili minne, na pembetatu nne. Mraba wa kati: Upande wake ni 4 cm. Mistarili miwili ya wima (juu na chini): Upana ni 4 cm na urefu ni 8 cm. Mistarili miwili ya mlalo (kushoto na kulia): Upana ni 11 cm na urefu ni 4 cm. Pembetatu nne (kwenye ncha za mikono): Msingi ni 4 cm na urefu ni 11 cm. Step 1: Kokotoa eneo la mraba wa kati. Eneo la mraba linapatikana kwa formula: upande × upande. A_mraba = 4 cm × 4 cm = 16 cm^2 Step 2: Kokotoa eneo la mistatili minne. Kuna mistatili miwili ya wima na miwili ya mlalo. Eneo la mstatili wa wima: 4 cm × 8 cm = 32 cm^2. Eneo la mistatili miwili ya wima: 2 × 32 cm^2 = 64 cm^2. Eneo la mstatili wa mlalo: 11 cm × 4 cm = 44 cm^2. Eneo la mistatili miwili ya mlalo: 2 × 44 cm^2 = 88 cm^2. Jumla ya eneo la mistatili: A_mistatili = 64 cm^2 + 88 cm^2 = 152 cm^2 Step 3: Kokotoa eneo la pembetatu nne. Eneo la pembetatu linapatikana kwa formula: (1)/(2) × msingi × urefu. Eneo la pembetatu moja: (1)/(2) × 4 cm × 11 cm = 2 cm × 11 cm = 22 cm^2. Eneo la pembetatu nne: A_pembetatu = 4 × 22 cm^2 = 88 cm^2 Step 4: Jumlisha maeneo yote kupata eneo la umbo zima. Jumla ya eneo ni jumla ya eneo la mraba, mistatili, na pembetatu. A_jumla = A_mraba + A_mistatili + A_pembetatu A_jumla = 16 cm^2 + 152 cm^2 + 88 cm^2 A_jumla = 256 cm^2 Eneo la umbo zima ni 256 cm^2. That's 2 down. 3 left today — send the next one.