Ta có tỉ số: \(\frac{{{V_{S.MNP}}}}{{{V_{S.ABC}}}} = \frac \cdot \frac \cdot \frac = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{8}\)

\( \Rightarrow {V_{S.MNP}} = \frac{1}{8}{V_{S.ABC}}\)

Tương tự ta cũng có tỉ số:

\(\frac{{{V_{S.MPQ}}}}{{{V_{S.ACD}}}} = \frac \cdot \frac \cdot \frac = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{8}\)

\( \Rightarrow {V_{S.MPQ}} = \frac{1}{8}{V_{S.ACD}}\)

Do đó: \[{V_{S.MNPQ}} = {V_{S.MNP}} + {V_{S.MPQ}} = \frac{1}{8}{V_{S.ABC}} + \frac{1}{8}{V_{S.ACD}}\]

\[ = \frac{1}{8}\left( {{V_{S.ABC}} + {V_{S.ACD}}} \right) = \frac{1}{8}{V_{S.ABCD}}\]