In the quadrilateral abcd, bd is the bisector of angle d. If c = 30, ad = 2, bc = 4 and cd = 6, then what is the area of ​the quadrilateral abcd?

Question

In the quadrilateral abcd, bd is the bisector of angle d. If c = 30, ad = 2, bc = 4 and cd = 6, then what is the area of ​​the quadrilateral abcd?

Answer 1

Let $BK$ be an altitude of $\Delta BDC$ and $BM$ be an altitude of $\Delta ABD$.

Thus, $BM=BK=\frac{4}{2}=2$ and $$S_{ABCD}=S_{\Delta ABD}+S_{\Delta CBD}=\frac{2\cdot2}{2}+\frac{2\cdot6}{2}=8.$$