Answer:
[tex]30 {cm}^{2} [/tex]
Solution,
[tex] \frac{bd}{cd} = \frac{ae}{ce} [/tex]
[tex] \frac{6}{8} = \frac{9}{8 + de} [/tex]
[tex]48 + 6(de) = 72[/tex]
[tex]6(de) = 72 - 48[/tex]
[tex]6(de) = 24[/tex]
[tex]de = \frac{24}{4} [/tex]
[tex]de = 4 \: [/tex]
CE = 8 + 4 = 12
Area of trapezoid ABDE:
Area of ∆ AEC - Area of ∆ BDC
[tex] = \frac{1}{2} \times 9 \times 12 - \frac{1}{2} \times 6 \times 8[/tex]
[tex] = 54 - 24[/tex]
[tex] = 30 \: {cm}^{2} [/tex]
Hope this helps...
Good luck on your assignment...
