In the given \(\triangle ABC\), \(DE\parallel BC\). If \(BC=8\) cm, \(DE=6\) cm and area of \(\triangle ADE=90\) cm², then what is the area of \(\triangle ABC\) (in cm²)?
160
Since \(DE\parallel BC\), triangles ADE and ABC are similar with ratio \(\frac{DE}{BC}=\frac{6}{8}=\frac{3}{4}\). The ratio of areas of similar triangles equals the square of the ratio of sides, so \(\frac{[ADE]}{[ABC]}=\frac{9}{16}\), giving \([ABC]=90\times\frac{16}{9}=160\) cm². No handwritten mark was visible on this question in the source sheet, so this answer is based purely on independent calculation.
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