area calculations

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

$\dfrac{a+b+8}{5+10}=\dfrac{a}{5}$ $\implies$ $5(a+b+8)=15a$ $\implies$ $a+b+8=3a$ $\implies$ $b+8=2a$ $\color{#D61F06}(1)$

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

$\dfrac{a+b+5}{8+10}=\dfrac{b}{8}$ $\implies$ $8(a+b+5)=18b$ $\implies$ $4a+4b+20=9b$ $\implies$ $4a+20=5b$ $\color{#D61F06}(2)$

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

$2(b+8)+20=5b$ $\implies$ $2b+16+20=5b$ $\implies$ $36=3b$ $\implies$ $12=b$

It follows that,

$2a=b+8=12+8=20$ $\implies$ $a=10$

Finally, the area of the yellow region is $a+b=10+12=$ $\boxed{22}$