In triunghiul BAA' unghiul A' are 90 grade, iar unghiul A are 45 grade => triunghi isoscel , cu AA'=BA'.
Pitagora > AB²=AA'²+BA'² => AB²=2AA'² => 12²= 2 AA'² => 144 = 2AA'² => AA'² = 72 => AA' = 6√2.
In triunghiul CAA' , unghiul A' are 90 grade, unghiul C are 30 grade , deci AA'=AC/2 => AC=2AA' => AC= 2* 6√2 => AC=12√2
Pitagora > AC²= AA'²+CA'² => (12√2)² = (6√2)² + CA'² => 144*2=36*2+CA'² => 288= 72 + CA'² => CA'² = 216 => CA' = 6√6 =>
BC= CA'+BA' dar BA' = AA' => BC=CA'+AA' => BC= 6√6+6√2
Perimetrul = AB+BC+AC = 12+(6√6+6√2)+12√2 = 12 + 6√6 + 18√2.
Aria = BC*AA' / 2 , unde AA' este inaltime. Aria = (6√6+6√2)*6√2/2 = (6√6+6√2)*3√2 = 6√2(√3+1)*3√2 = 18*2 * (√3+1) = 36(√3+1)
