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
Hatua ya 1: Tambua maumbo na vipimo vilivyotolewa. Mchoro unaonyesha mstatili wenye urefu H = 10 \, dm. Ndani ya mstatili huu, kuna maumbo mawili yanayofanana kama matao. Tunachukulia kuwa haya ni nusu-duara. Sehemu zilizotiwa kivuli ni zile sehemu za mstatili ambazo hazijafunikwa na nusu-duara mbili na eneo la mstatili lisilotiwa kivuli katikati yao. Hatua ya 2: Kokotoa rediasi ya nusu-duara. Kipenyo cha kila nusu-duara ni sawa na urefu wa mstatili, D = H = 10 \, dm. Rediasi ya kila nusu-duara ni r = (D)/(2) = 10 \, dm2 = 5 \, dm. Hatua ya 3: Kokotoa eneo la nusu-duara mbili. Eneo la nusu-duara moja ni (1)/(2) r^2. Eneo la nusu-duara mbili ni A_nusu-duara = 2 × (1)/(2) r^2 = r^2. Badilisha r = 5 \, dm: A_nusu-duara = (5 \, dm)^2 = 25 \, dm^2 Hatua ya 4: Bainisha eneo lote la mstatili. Upana wa kila nusu-duara ni kipenyo chake, D = 10 \, dm. Acha upana wa eneo la mstatili lisilotiwa kivuli katikati ya nusu-duara mbili uwe x. Upana wote wa mstatili utakuwa W = D + x + D = 10 \, dm + x + 10 \, dm = (20 + x) \, dm. Urefu wa mstatili ni H = 10 \, dm. Eneo lote la mstatili ni A_mstatili = W × H = (20 + x) \, dm × 10 \, dm = (200 + 10x) \, dm^2. Hatua ya 5: Kokotoa eneo la sehemu iliyotiwa kivuli. Eneo lililotiwa kivuli ni eneo lote la mstatili ukitoa eneo la nusu-duara mbili na eneo la mstatili lisilotiwa kivuli katikati (A_kati\_isiyotiwa\_kivuli = 10x \, dm^2). A_iliyotiwa\_kivuli = A_mstatili - A_nusu-duara - A_kati\_isiyotiwa\_kivuli A_iliyotiwa\_kivuli = (200 + 10x) \, dm^2 - 25 \, dm^2 - 10x \, dm^2 A_iliyotiwa\_kivuli = (200 - 25) \, dm^2 Hatua ya 6: Badilisha thamani ya = 3.14 na kokotoa jibu la mwisho. A_iliyotiwa\_kivuli = (200 - 25 × 3.14) \, dm^2 A_iliyotiwa\_kivuli = (200 - 78.5) \, dm^2 A_iliyotiwa\_kivuli = 121.5 \, dm^2 That's 2 down. 3 left today — send the next one.