As we know that area of parallelogram ABCD is 48 units.
And the area of parallelogram ABCD can be calculated as:
[tex]\begin{gathered} A_{ABCD}=(BA)\times h \\ 48=BA\times h \\ h=\frac{48}{BA} \end{gathered}[/tex]
Now given that BA=AE
So
[tex]\begin{gathered} BE=BA+AE \\ BE=2BA \end{gathered}[/tex]
Now area of trapezoid BCDE is:
[tex]\begin{gathered} A_{BCDE}=\frac{1}{2}\times(CD+BE)\times h \\ A_{BCDE}=\frac{1}{2}\times(BA+BE)\times h \\ A_{BCDE}=\frac{1}{2}\times(BA+2BA)\times h \\ A_{BCDE}=\frac{1}{2}\times3BA\times\frac{48}{BA} \\ A_{BCDE}=\frac{1}{2}\times3\times48 \\ A_{BCDE}=72 \end{gathered}[/tex]
So area of BCDE is 72 unit.
