A square with side length 3 is inscribed in an isosceles triangle with one side of the square along the base of the triangle. A square with side length 2 has two vertices on the other square and the other two on sides of the triangle, as shown. What is the area of the triangle?[asy]
//diagram by kante314
draw((0,0)--(8,0)--(4,8)--cycle, linewidth(1.5));
draw((2,0)--(2,4)--(6,4)--(6,0)--cycle, linewidth(1.5));
draw((3,4)--(3,6)--(5,6)--(5,4)--cycle, linewidth(1.5));
[/asy](<spanclass=′latex−bold′>A</span>)1941(<spanclass=′latex−bold′>B</span>)2041(<spanclass=′latex−bold′>C</span>)2143(<spanclass=′latex−bold′>D</span>)2221(<spanclass=′latex−bold′>E</span>)2343