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

Answer: Option B

Diagonal of a square = (a + b)
∴ side of square = $$\frac{\left(a+b\right)}{\sqrt{2}}$$
∴ Area of square = (side)²
$$\begin{array}{rl}& ={\left(\frac{a+b}{\sqrt{2}}\right)}^2\\ & =\frac{1}{2}\left(a^2+b^2+2ab\right)\\ & =\frac{1}{2}\left(a^2+b^2\right)+ab\end{array}$$