Question

Answer 1

AB//CD

=>\(\frac{AB}{CD}=\frac{OA}{OC}=\frac{OB}{OD}=\frac34\)

Ta có: \(\frac{OA}{OC}=\frac34\)

=>\(\frac{S_{DOA}}{S_{DOC}}=\frac34\)

=>\(S_{DOA}=\frac34\times S_{DOC}\)

Ta có: \(\frac{OB}{OD}=\frac34\)

=>\(\frac{S_{OBC}}{S_{OCD}}=\frac34\)

=>\(S_{OBC}=\frac34\times S_{OCD}\)

Ta có: \(\frac{OB}{OD}=\frac34\)

=>\(\frac{S_{AOB}}{S_{AOD}}=\frac34\)

=>\(S_{AOB}=\frac34\times S_{AOD}=\frac34\times\frac34\times S_{DOC}=\frac{9}{16}\times S_{COD}\)

Ta có: \(S_{AOB}+S_{BOC}+S_{AOD}+S_{DOC}=S_{ABCD}\)

=>\(S_{DOC}+\frac34\times S_{DOC}+\frac34\times S_{DOC}+\frac{9}{16}\times S_{DOC}=S_{ABCD}\)

=>\(S_{DOC}\times\left(1+\frac34+\frac34+\frac{9}{16}\right)=128\)

=>\(S_{DOC}\times\left(\frac{16}{16}+\frac{12}{16}+\frac{12}{16}+\frac{9}{16}\right)=128\)

=>\(S_{DOC}\times\frac{49}{16}=128\)

=>\(S_{DOC}=128:\frac{49}{16}=128\times\frac{16}{49}=\frac{2048}{49}\left(\operatorname{cm}^2\right)\)