Use double integration to calculate the area that liew between the curves

$\displaystyle \sqrt{x} + \sqrt{y} = \sqrt{a}$$\displaystyle and x + y = a, a > 0$This is what i have done , between the limits on the y = a-x and y = 0 and for x = a and 0$\displaystyle \iint dy dx \int a- x dx = ax - \frac{{x}^{ 2} }{2 } = {a}^{ 2} - \frac{{a}^{ 2} }{2 } = \frac{{a}^{ 2} }{2 }$ But according to my text book the answer is $\displaystyle \frac{{a}^{ 2} }{3 }$