Large MDF shelf support

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Hi there,

We have put up a shelf in an alcove in our loft. As it's a fairly large gap and an odd shape we had to use oak veneered MDF to make it work in one piece.
On top of the shelf will sit a projector of around 7kg, a playstation and some other smaller bits and bobs like small lights and plants. We have already put in battens around the inside edge of the alcove for the shelf to sit on, but it's currently lacking any support in the middle or front. As it's a sort of trapezoid we're not sure of the best way to support it. We'd rather not use brackets to maintain a kind of floating look, so would rather use additional wooden battens if there's a way of arranging them for good support.

Dimensions are 200cm wide x 24 & 75cm deep (left and right sides different depths) and the diagonal is 206cm. Here's some pictures attached.

Thanks for any help!
 

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