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APMOPS 2009 Question 27

APMOPS · APMOPS 2009

Question 27

The diagram shows a trapezium $ABCD$. The length of $AB$ is $2\frac12$ times that of $CD$, and the areas of triangles $OAB$ and $OCD$ are 20 cm$^2$ and 14 cm$^2$, respectively. Given that the trapezium has area $x$ cm$^2$, find $x$.

Question illustration

Source note: the drawn diagonal intersection is inconsistent with the stated areas; this item requires review. The literal written data and the issue are discussed in the solution.