Răspuns:
A(ABC) = AO×BC/2
AO = √AC² - (BC/2)² = √100 - 64 = √36 = 6 dm
A(ABC) = 6dm×16dm/2 = 48 dm²
CD/CB = 1/4 =>A(ADO)/A(ABC) = 1/4 => A(ADO) = 48/4 = 12 dm²
A(BCM) = MO×BC/2
MO = √CM² - (BC/2)² = √80 - 64 = √16 = 4 dm
A(BCM) = 4dm×16dm/2 = 32 dm²
CD/CB = 1/4 =>A(DMO)/A(BCM) = 1/4 => A(DMO) = 32/4 = 8 dm²
A(ADM) = A(ADO) + A(DMO) = 20 dm²
Obs. Mediana imparte triunghiul in 2 triunghiuri cu arii egale.
