Answer:
8 square units and [tex]\frac{40}{3}[/tex] square units
Step-by-step explanation:
The area of the triangle ABC is 24 square units.
1. Triangles ABC and FBG are similar with scale factor [tex]\frac{1}{3},[/tex] then
[tex]\dfrac{A_{\triangle FBG}}{A_{\triangle ABC}}=\dfrac{1}{9}\Rightarrow A_{\triangle FBG}=\dfrac{1}{9}\cdot 24=\dfrac{8}{3}\ un^2.[/tex]
2. Triangles ABC and DBE are similar with scale factor [tex]\frac{2}{3},[/tex] then
[tex]\dfrac{A_{\triangle DBE}}{A_{\triangle ABC}}=\dfrac{4}{9}\Rightarrow A_{\triangle DBE}=\dfrac{4}{9}\cdot 24=\dfrac{32}{3}\ un^2.[/tex]
3. Thus, the area of the quadrilateral DFGE is
[tex]A_{DFGE}=A_{\triangle DBE}-A_{\triangle FBG}=\dfrac{32}{3}-\dfrac{8}{3}=8\ un^2.[/tex]
and the area of the quadrilateral ADEC is
[tex]A_{ADEC}=A_{\triangle ABC}-A_{\triangle DBE}=24-\dfrac{32}{3}=\dfrac{40}{3}\ un^2.[/tex]
