a) $\dfrac{d_{A,(SBC)}}{d_{A',(SB'C)}}=\dfrac{AS}{A'S}=2$
$S_{AB'C}=SB'.SA.\sin\widehat{B'SC}$
$S_{ABC}=SB.SA.\sin\widehat{BSC}$
$\Rightarrow \dfrac{S_{ABC}}{S_{AB'C}}=\dfrac{SB.SA.\sin\widehat{BSC}}{SB'.SA.\sin\widehat{B'SC}}=\dfrac{SB}{SB'}=2$
$V_ASBC=\dfrac{1}{3}d_{A,(SBC)}.S_{ABC}$
$V_ASB'C=\dfrac{1}{3}d_{A,(SB'C)}.S_{AB'C}$
$\Rightarrow \dfrac{V_ASBC}{V_ASB'C}=4$
$\Rightarrow \dfrac{V_ASB'C}{V_ASBC}=\dfrac{1}{4}$
16) $V_{A'ABC}=\dfrac{1}{3}A'A.S_{ABC}=\dfrac{1}{3}A'A.\dfrac{1}{2}S_{ABCD}=\dfrac{1}{6}A'A.S_{ABCD}=\dfrac{1}{6}.V$
