If the length of a diagonal of a square is ( a+b ), then the area of the square is:

A

$$a^{2}+b^{2}$$

B

$$\frac{1}{2} \left(a^{2}+b^{2}\right)$$

C

$$\frac{1}{2} \left(a^{2}+b^{2}\right)+ab$$

D

$$a^{2}+b^{2}+2ab$$