Calculate triangle area

[math_Lover]

In the rectangle ABCD the side BC is divided into three equal parts by points E and F (see the figure): |BE| = |EF| = |FC|.
The point M divides the side AD into two equal parts (|AM| = |MD|).
The diagonal BD intersects straight lines EM and FM in points K and L respectively.
Find the area of the triangle MKL if the area of the rectangle ABCD equals 280.

 

[Deleted member 4993]

In the rectangle ABCD the side BC is divided into three equal parts by points E and F (see the figure): |BE| = |EF| = |FC|.
The point M divides the side AD into two equal parts (|AM| = |MD|).
The diagonal BD intersects straight lines EM and FM in points K and L respectively.
Find the area of the triangle MKL if the area of the rectangle ABCD equals 280.

View attachment 23550

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[Dr.Peterson]

In the rectangle ABCD the side BC is divided into three equal parts by points E and F (see the figure): |BE| = |EF| = |FC|.
The point M divides the side AD into two equal parts (|AM| = |MD|).
The diagonal BD intersects straight lines EM and FM in points K and L respectively.
Find the area of the triangle MKL if the area of the rectangle ABCD equals 280.

View attachment 23550

I can think of several approaches you could take. For example, it is clear that the proportions of ABCD have no effect, so you could choose convenient dimensions and work out coordinates; or (almost equivalently) you could drop verticals from K and L and work with similar triangles.

What methods have you been learning? Try whatever method you like, and show us your start, so we can guide you further.