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In the figure seg PQ|| seg DE, A(DeltaP...

In the figure seg `PQ||` seg DE, `A(DeltaPQF)=20` units `PF=2DP`,then find `A(square DPQE)` by completing the following activity:

Activity: `A(DeltaPQF)=20` sq units, `PF=2DP`.
Let us assume `DP=x`
`:.PF=2x`
`DF=DE+square=square+square=3x`
In `DeltaFDE` and `DeltaFPQ`.
`/_FDE~=/_square` ..........(Corresponding angles)
`/_FED~=/_square` .....(Corresponding angles)
`:.DeltaFDE~DeltaFPQ` .....(AA test)
`:.(A(DeltaFDE))/(A(DeltaFPQ))=(square)/(square)=((3x)^(2))/((2x)^(2))=9/4`
`A(DeltaFDE)=9/4A(DeltaFPQ)=9/4xxsquare=square`
`A(squareDPQE)=A(DeltaFDE)-A(DeltaFPQ)`
`=square-square`
`=square`

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