Question : What is the area of the shaded region?
$$Area\ of\ square\ =\ 20^2\ =\ 20\ \cdot\ 20\ =\ 400$$
$$Area\ of\ top\ traingle\ enclosed\ by\ lenght\ a\ =\ 0.5\ \cdot\ a^2$$
$$Area\ of\ bottom\ traingle\ enclosed\ by\ lenght\ b\ =\ 0.5\ \cdot\ b^2$$
$$Area\ of\ shaded\ region\ =\ 400\ -\ 0.5\ \left(a^2\ +\ b^2\right)$$
$$Statement\ 1\ =\ \left(a\ +\ b\right)^2\ =\ 49$$
$$Therefore,\ \ a^2\ +\ b^2\ +\ 2ab\ =\ 49$$
We don't know the value of 2ab,
Hence statement 1 is NOT SUFFICIENT.

$$Statement\ 2\ :\ \ \left(a^2\right)\ +\ \left(b^2\right)=\ 25$$
$$Area\ of\ shaded\ region\ =\ 400\ -\ 0.5\ \left(a^2\ +\ b^2\right)$$
= 400 - 0.5 (25)
= 400 - 12.5
= 383

Hence, statement 2 is SUFFICIENT.
Option B is CORRECT.