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
Step 1: Tambua vipimo vya prismu. Prismu ina msingi wa pembetatu. • Pandeti za pembetatu ni 20 cm, 21 cm, na 29 cm. • Urefu wa prismu (urefu wa pande za mstatili) ni 31 cm. Kumbuka kuwa 20^2 + 21^2 = 400 + 441 = 841, na 29^2 = 841. Hii inamaanisha pembetatu ya msingi ni pembetatu mraba, na pande 20 cm na 21 cm ni msingi na urefu wake. Step 2: Kokotoa eneo la nyuso mbili za msingi (pembetatu). Eneo la pembetatu moja (A_pembetatu) = (1)/(2) × msingi × urefu A_pembetatu = (1)/(2) × 20 cm × 21 cm A_pembetatu = 10 cm × 21 cm = 210 cm^2 Eneo la nyuso mbili za msingi (A_misingi) = 2 × A_pembetatu A_misingi = 2 × 210 cm^2 = 420 cm^2 Step 3: Kokotoa eneo la nyuso tatu za pembeni (mstatili). Kila uso wa pembeni ni mstatili wenye urefu wa 31 cm na upana sawa na moja ya pande za pembetatu ya msingi. • Eneo la mstatili wa kwanza (A_mstatili1) = 20 cm × 31 cm = 620 cm^2 • Eneo la mstatili wa pili (A_mstatili2) = 21 cm × 31 cm = 651 cm^2 • Eneo la mstatili wa tatu (A_mstatili3) = 29 cm × 31 cm = 899 cm^2 Jumla ya eneo la nyuso za pembeni (A_pembeni) = A_mstatili1 + A_mstatili2 + A_mstatili3 A_pembeni = 620 cm^2 + 651 cm^2 + 899 cm^2 = 2170 cm^2 Step 4: Kokotoa jumla ya eneo la uso la prismu. Jumla ya eneo la uso (A_jumla) ni jumla ya eneo la nyuso mbili za msingi na eneo la nyuso tatu za pembeni. A_jumla = A_misingi + A_pembeni A_jumla = 420 cm^2 + 2170 cm^2 A_jumla = 2590 cm^2 2590 cm^2 Last free one today — make it count tomorrow, or type /upgrade for unlimited.