Giải thích các bước giải:
a.Xét $\Delta FAE,\Delta FDC$ có:
Chung $\hat F$
$\widehat{FAE}=\widehat{FDC}$ vì $AB//CD$
$\to\Delta FAE\sim\Delta FDC(g.g)(1)$
Xét $\Delta FAE,\Delta EBC$ có:
$\widehat{AEF}=\widehat{BEC}$
$\widehat{AFE}=\widehat{ECB}$ vì $AD//BC$
$\to\Delta FAE\sim\Delta CBE(g.g)(2)$
Từ $(1) , (2)\to\Delta FDC\sim\Delta CBE$
b.Ta có $\dfrac{EA}{AB}=\dfrac13\to AB=3AE=12$
Ta có $AD//BC$
$\to \dfrac{BC}{AF}=\dfrac{BE}{EA}=2\to BC=2AF=2\cdot 2=4$
$\to P_{ABCD}=2(AB+BC)=2(12+4)=32$