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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.

 Dec 17, 2019
 #1
avatar+120 
+2

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

\(c+d=8-1=7\)

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 Dec 17, 2019
 #2
avatar+24430 
+3

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.

 

\(\begin{array}{|rcll|} \hline \mathbf{CDA + ABC} &=& \mathbf{DAB + BCD} \\ 2 + 6 &=& 1 + BCD \\ 8 &=& 1 + BCD \\ BCD &=& 8-1 \\ \mathbf{BCD} &=& \mathbf{7} \\ \hline \end{array}\)

 

laugh

 Dec 17, 2019
 #3
avatar+109752 
+1

Nice, Gadfly and heureka    !!!

 

 

 

cool cool cool

CPhill  Dec 17, 2019
 #4
avatar+24430 
+1

Thank you, CPhill !

 

laugh

heureka  Dec 18, 2019

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