Answer
A=96
Work Step by Step
Triangle ABC has a height of 5 and base of 12. Knowing pythagorean triples, its hypotenuse, AC, must be 13. Since this is also the hypotenuse of triangle AEC whose height is also 5, the base, EC of triangle AEC must be 12. Given that DC and DE are congruent, DEC is an isosceles right triangle with a hypotenuse of length 12. Therefore the sides DE and DC of the triangle must have a length of 6$\sqrt 2$.
A=.5(12)(5)+.5(12)(5)+.5(6$\sqrt 2$)$^2$
A=30+30+36
A=96
