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.
ScanSolve AI Answer
Huu hapa ni ufumbuzi wa swali la 31: Ili kupata eneo lote la uso wa 'wedge' (prismu ya pembetatu), tunahitaji kuhesabu eneo la nyuso zake zote: nyuso mbili za pembetatu na nyuso tatu za mstatili. Step 1: Tafuta urefu wa hypotenuse ya msingi wa pembetatu. Msingi wa pembetatu ni pembetatu ya pembe mraba yenye pande za 6 cm na 8 cm. Tunatumia theorem ya Pythagoras: c^2 = a^2 + b^2. c = sqrt(6^2 + 8^2) c = sqrt(36 + 64) c = sqrt(100) c = 10 cm Step 2: Kokotoa eneo la nyuso mbili za pembetatu. Eneo la pembetatu moja ni (1)/(2) × base × height. Eneo la pembetatu moja = (1)/(2) × 8 cm × 6 cm = 24 cm^2 Eneo la pembetatu mbili = 2 × 24 cm^2 = 48 cm^2 Step 3: Kokotoa eneo la nyuso tatu za mstatili. Urefu wa 'wedge' ni 9 cm. • Eneo la mstatili wa chini: 8 cm × 9 cm = 72 cm^2 • Eneo la mstatili wa upande: 6 cm × 9 cm = 54 cm^2 • Eneo la mstatili wa juu uliopinda (hypotenuse × urefu): 10 cm × 9 cm = 90 cm^2 Step 4: Jumlisha maeneo yote ili kupata eneo lote la uso. Eneo lote la uso = 48 cm^2 + 72 cm^2 + 54 cm^2 + 90 cm^2 Eneo lote la uso = 264 cm^2 Eneo lote la uso wa 'wedge' ni 264 cm^2. Tuma swali linalofuata 📸