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
Calister, hebu tutatue swali la 8. Step 1: Tafuta urefu wa upande mmoja wa rombasi. Rombasi ina pande nne zenye urefu sawa. Mzunguko (perimeter) wa rombasi hutolewa na fomula P = 4s, ambapo s ni urefu wa upande mmoja. Tunapewa mzunguko P = 40 mita. 4s = 40 Gawanya pande zote mbili kwa 4: s = (40)/(4) s = 10 m Hivyo, urefu wa kila upande wa rombasi ni mita 10. Step 2: Tumia theoremu ya Pythagoras kutafuta nusu ya diagonal ya pili. Tunajua kwamba diagonals za rombasi hugawana kila mmoja kwa pembe za kulia. Hii inaunda pembetatu nne za kulia ndani ya rombasi. Urefu wa diagonal moja (AC) ni mita 16. Hivyo, nusu ya diagonal hii ni AO = (16)/(2) = 8 mita. Upande wa rombasi (s) ni hypotenuse ya pembetatu hizi za kulia. Hebu tuchukue pembetatu ya kulia iliyoundwa na nusu ya diagonals na upande mmoja wa rombasi. Tuna s = 10 m (hypotenuse) na AO = 8 m (moja ya miguu). Hebu BO iwe mguu mwingine. Kwa theoremu ya Pythagoras: AO^2 + BO^2 = s^2. 8^2 + BO^2 = 10^2 64 + BO^2 = 100 Toa 64 kutoka pande zote mbili: BO^2 = 100 - 64 BO^2 = 36 Chukua mzizi wa mraba wa pande zote mbili: BO = sqrt(36) BO = 6 m Step 3: Tafuta urefu kamili wa diagonal ya pili. Diagonal ya pili (d_2) ni mara mbili ya BO. d_2 = 2 × BO d_2 = 2 × 6 m d_2 = 12 m Step 4: Kokotoa eneo la rombasi. Eneo la rombasi (A) hutolewa na fomula A = (1)/(2) d_1 d_2, ambapo d_1 na d_2 ni urefu wa diagonals. Tuna d_1 = 16 m na d_2 = 12 m. A = (1)/(2) (16 m)(12 m) A = 8 × 12 m^2 A = 96 m^2 Eneo lote la nafasi ya kuketi ni: 96 m^2 3 done, 2 left today. You're making progress.