Your idea is right, but it is a bit difficult to expand BA. Because angle BAE+ angle AED=270 degrees, angle ABD+ angle EDB=90 degrees. Triangle PBD is a right triangle. If PE is X in the triangle PAE, then PA= root number 64-x 2, and (4+X)2+(3+ root number 64-x 2) in the triangle PBD. 2 = 169 is simplified to 25x2-320x+1024 (5x-32) 2 = 0x = 32/5pa = 24/5, so the area of quadrilateral ABDE is (4+32)/5x3+24/5.

Adopt it