smc

Since they tell us that AB=AG and that angle A is a right angle, triangle ABG is a 45-45-90 triangle. Thus we can find the legs of the triangle by dividing $20$ (the hypotenuse) by $\sqrt{2}$. Both legs have length $10\sqrt{2}$, so the area of the right triangle is $100$. The rectangle is simple, just $20\times 10$, so the area is 200. Adding these areas, we get $300$ as the total area. $\boxed{300}$