You can use the method of coordinate system, with B as the center, BA as the Y axis and BC as the X axis, write the analytical formula of DE, set the point P coordinate, then list the area equation, and then find the maximum value.

The analytical formula of DE: y=- 1/2x+ 10.

Let P(X,-1/2X+ 10)

Find the range of x, 4

The area is X *( 1/2X+ 10). Just use the quadratic function to find the maximum value.

When x is 8, y is 48.