A square with sides of length $2$ units is constructed on a right triangle with a hypotenuse of length $2\sqrt{5}$ units to form the figure shown. What is the total area of the figure, in square units?

Use pythagorean to find the missing side of the triangle sqrt(20-4)= 4 so the area of the triangle is 4 and the square is also four. Total area is 8 square units.