12) $\widehat{(ACC'A'),(ABC)}=\widehat{AA',(ABC)}$
$=\widehat{(AA',AH)}=\widehat{A'AH}=45^o$
$\Rightarrow \Delta $ vuông $A'AH$ cân đỉnh A
$\Rightarrow A'H=AH=\dfrac{a}{2}$
$V=A'H.S_{\Delta ABC}=\dfrac{a}{2}\dfrac{1}{2}a.a.\sin60^o$
$=\dfrac{a^3\sqrt3}{8}$
13) Gọi $I$ là trung điểm của $AB$
Áp dụng định lý Pitago vào $\Delta $ vuông $A'$
$A'I=AA'^2-AI^2=a^2-(\dfrac{a}{2})^2$
$\Rightarrow A'I=\dfrac{a\sqrt3}{2}$
$S_{IKCD}=S_{ABCD}-S_{AID}-S_{BIK}$
$=a^2-\dfrac{1}{2}\dfrac{a}{2}a-\dfrac{1}{2}\dfrac{a}{2}\dfrac{a}{2}$
$=\dfrac{5a^2}{8}$
$V=A'I.S_{IKCD}=\dfrac{a\sqrt3}{2}.\dfrac{5a^2}{8}=\dfrac{5a^3\sqrt3}{16}$
