Question

The area of ABCD IS 48. If BA = AE and CD = AB find the area of trapezoid BCDE.

Answer 1

As we know that area of parallelogram ABCD is 48 units.

And the area of parallelogram ABCD can be calculated as:

`\begin{gathered} A_(ABCD)=(BA)* h \\ 48=BA* h \\ h=(48)/(BA) \end{gathered}`

Now given that BA=AE

So

`\begin{gathered} BE=BA+AE \\ BE=2BA \end{gathered}`

Now area of trapezoid BCDE is:

`\begin{gathered} A_(BCDE)=(1)/(2)*(CD+BE)* h \\ A_(BCDE)=(1)/(2)*(BA+BE)* h \\ A_(BCDE)=(1)/(2)*(BA+2BA)* h \\ A_(BCDE)=(1)/(2)*3BA*(48)/(BA) \\ A_(BCDE)=(1)/(2)*3*48 \\ A_(BCDE)=72 \end{gathered}`

So area of BCDE is 72 unit.