Square2d

The green triangle is isosceles, with equal sides of length $\sqrt {(12+6)^2+6^2}=6\sqrt {10}$ each and base of length $\sqrt {12^2+12^2}=12\sqrt {2}$ . Hence it's height is $\sqrt {(6\sqrt {10})^2-(6\sqrt 2)^2}=12\sqrt 2$ , and area is $\dfrac{1}{2}\times {12\sqrt 2}\times {12\sqrt2}=\boxed {144}$

By Pythagorean Theorem,

$a = \sqrt{12^2 + 12^2} = 12\sqrt{2}$

$b = \sqrt{18^2 + 6^2} = 6\sqrt{10}$

$c = \sqrt{18^2 + 6^2} = 6\sqrt{10}$

The area can be found using any method. The area is $\boxed{144}$