SEAMO 2027 - Paper E - SET 10 - Self-study Question 19

Question 19

In triangle $ABC$, $D$ lies on $AB$ and $DE\parallel BC$, with $E$ on $AC$. Point $F$ lies on $BC$ and $DF\parallel AC$. The areas of triangles $ADE$ and $DBF$ are $m,n$, respectively. Find the area of quadrilateral $DECF$.

Question illustration

$(2\sqrt m+\sqrt n)^2$
$(\sqrt m+2\sqrt n)^2$
$(\sqrt m+\sqrt n)^2$
$m+\sqrt{mn}+n$
$2\sqrt{mn}$