In convex quadrialteral ABCD, the area of triangle DAB is 1, that of triangle ABC is 6, and that of triangle CDA is 2. Find the area of triangle BCD.
+121 
Since area of DAB, ABC, and CDA are 1, 6, and 2, respectively, we have
\(a+b=1\),
\(b+c=6\), and
\(a+d=2\).
We need to find the area of BCD, that is \(c+d\).
Add equations two and three to get
\(a+b+c+d=8\).
Subtract equation one to get
\(c+d=8-1=7\)
+26367 In convex quadrialteral ABCD, the area of triangle DAB is 1, that of triangle ABC is 6, and that of triangle CDA is 2.
Find the area of triangle BCD.
\(\begin{array}{|rcll|} \hline \mathbf{CDA + ABC} &=& \mathbf{DAB + BCD} \\ 2 + 6 &=& 1 + BCD \\ 8 &=& 1 + BCD \\ BCD &=& 8-1 \\ \mathbf{BCD} &=& \mathbf{7} \\ \hline \end{array}\)
