a: \(S_{ABC}=\dfrac{1}{2}\cdot15\cdot34=17\cdot15=255\left(cm^2\right)\)
b: BN=1/2NM=1/2*3/4MC=3/8MC
BN+NM+MC=BC
=>BC=3/8MC+3/4MC+MC=17/8MC=17/8*8/3BN=17/3BN
=>\(S_{ABC}=\dfrac{17}{3}\cdot S_{ABN}\)
=>\(S_{ABN}=255:\dfrac{17}{3}=45\left(cm^2\right)\)