AHSME 1951 Problem 3

If the length of a diagonal of a square is $a + b$, then the area of the square is: $\mathrm{(A) \ (a+b)^2 } \mathrm{(B) \ \frac{1}{2}(a+b)^2 } \mathrm{(C) \ a^2+b^2 } \mathrm{(D) \ \frac {1}{2}(a^2+b^2) } \mathrm{(E) \ \text{none of these} }$