Answer:
8 square units and [tex]\frac{40}{3}[/tex] square units.
Step-by-step explanation:
Consider triangle aBc. In this triangle, AD = DF = FB, DE || FG || AC and area of the triangle is 24 square units.
1. Triangles BFG and BAC are similar with the scale factor of 1/3, then
[tex]A_{BFG}=\left(\dfrac{1}{3}\right)^2 \cdot A_{ABC}=\dfrac{1}{9}\cdot 24=\dfrac{8}{3}\ un^2.[/tex]
2. Triangles BDE and BAC are similar with the scale factor of 2/3, then
[tex]A_{BDE}=\left(\dfrac{2}{3}\right)^2 \cdot A_{ABC}=\dfrac{4}{9}\cdot 24=\dfrac{32}{3}\ un^2.[/tex]
Then the area of the trapezoid DFGE is
[tex]A_{DFGE}=A_{BDE}-A_{BGF}=\dfrac{32}{3}-\dfrac{8}{3}=8\ un^2.[/tex]
and the area of the trapezoid ADEC is
[tex]A_{ADEC}=A_{ABC}-A_{BDE}=24-\dfrac{32}{3}=\dfrac{40}{3}\ un^2.[/tex]
