Bài 21:
Vì AB//CD
nên \(\frac{OA}{OC}=\frac{OB}{OD}=\frac{AB}{CD}=\frac14\)
\(\frac{OA}{OC}=\frac14\)
=>\(\frac{S_{BOA}}{S_{BOC}}=\frac14\)
=>\(S_{BOC}=4\times S_{BOA}\)
Vì \(\frac{OB}{OD}=\frac14\)
nên \(\frac{S_{BOC}}{S_{DOC}}=\frac14\)
=>\(S_{DOC}=4\times S_{BOC}=4\times4\times S_{BOA}=16\times S_{BOA}\)
Ta có: \(S_{DOC}-S_{BOA}=1995\)
=>\(16\times S_{BOA}-S_{BOA}=1995\)
=>\(15\times S_{BOA}=1995\)
=>\(S_{BOA}=\frac{1995}{15}=133\left(\operatorname{cm}^2\right)\)
\(S_{BOC}=4\times133=532\left(\operatorname{cm}^2\operatorname{}^{}\right)\)
\(S_{DOC}=16\times133=2128\left(\operatorname{cm}^2\right)\)
Vì \(\frac{OB}{OD}=\frac14\)
nên \(\frac{S_{BOA}}{S_{AOD}}=\frac14\)
=>\(S_{AOD}=4\times S_{BOA}=4\times133=532\left(\operatorname{cm}^2\right)\)
\(S_{ABCD}=S_{OAB}+S_{OBC}+S_{ODC}+S_{OAD}\)
\(=133+532+532+2128=3325\left(\operatorname{cm}^2\right)\)
