calculation of area -1

Consider the diagram. Recall that the areas of triangles with equal altitudes are proportional to the bases of the triangles. We have, $\dfrac{AD}{DB}=\dfrac{A_{CDA}}{A_{CDB}}=\dfrac{A_{XDA}}{A_{XDB}}$

$\dfrac{a+b+4}{3+6}=\dfrac{a}{3}$ $\implies$ $3(a+b+4)=9a$ $\implies$ $a+b+4=3a$ $\implies$ $b+4=2a$ $\color{#D61F06}(1)$

$\dfrac{AE}{EC}=\dfrac{A_{ABE}}{A_{BEC}}=\dfrac{A_{AXE}}{A_{EXC}}$

$\dfrac{a+b+3}{4+6}=\dfrac{b}{4}$ $\implies$ $4(a+b+3)=10b$ $\implies$ $2a+2b+6=5b$ $\implies$ $2a+6=3b$ $\color{#D61F06}(2)$

Substitute $\color{#D61F06}(1)$ in $\color{#D61F06}(2)$ , we have

$b+4+6=3b$ $\implies$ $10=2b$ $\implies$ $5=b$

It follows that,

$2a=b+4=5+4=9$ $\implies$ $a=4.5$

Finally, the area of the yellow region is $a+b=4.5+5=$ $\boxed{9.5}$