AMC 10 2021-fall-b Problem 13

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?

$(\textbf{A})\: 19\frac14 (\textbf{B}) \: 20\frac14 (\textbf{C}) \: 21 \frac34 (\textbf{D}) \: 22\frac12 (\textbf{E}) \: 23\frac34$