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Kneel for standard answers and processes ... the ninth grade mathematics education version is complete.
Solution: √△ACB is RT△, BC=AC=3√2.

△ ACB is an isosceles right triangle.

CF = x

∴AE=EP=CF=x PF=BF=3√2-x

The ∴ area of a rectangle PECF =PF*CF=(3√2-x)x

The area of RT△AEP =AE*EP/2=x? /2

The area of RT△PFB =PF*FB/2=(3√2-x)? /2