四面体の体積

\(\normalsize Tetrahedron\\ (1)\ volume:\\ \hspace{40px} V=\sqrt{V^2}\\ \hspace{40px} V^2=\frac{1}{144}[a_1^2a_5^2(a_2^2+a_3^2+a_4^2+a_6^2-a_1^2-a_5^2)\\ \hspace{60px}+a_2^2a_6^2(a_1^2+a_3^2+a_4^2+a_5^2-a_2^2-a_6^2)\\ \hspace{60px}+a_3^2a_4^2(a_1^2+a_2^2+a_5^2+a_6^2-a_3^2-a_4^2)\\ \hspace{60px}-a_1^2a_2^2a_4^2-a_2^2a_3^2a_5^2-a_1^2a_3^2a_6^2-a_4^2a_5^2a_6^2]\\ (2)\ surface\ area:\\ \hspace{40px} S=\sqrt{s_1(s_1-a_1)(s_1-a_2)(s_1-a_4)}\\ \hspace{60px}+\sqrt{s_2(s_2-a_2)(s_2-a_3)(s_2-a_5)}\\ \hspace{60px}+\sqrt{s_3(s_3-a_3)(s_3-a_6)(s_3-a_1)}\\ \hspace{60px}+\sqrt{s_4(s_4-a_4)(s_4-a_5)(s_4-a_6)}\\ \hspace{40px}s1={\large \frac{a_1+a_2+a_4}{2}},\ s2={\large \frac{a_2+a_3+a_5}{2}}\\ \hspace{40px}s3={\large \frac{a_3+a_6+a_1}{2}},\ s4={\large \frac{a_4+a_5+a_6}{2}}\\ \)