# A geometry problem by Nikkil V

Geometry Level 3

$$ABCD$$ is a rectangle.

$$E$$ is a point on $$AD$$ such that $$BE= 31\text{ cm}.$$
$$F$$ is a point on $$DC$$ such that $$FB = 40\text{ cm}.$$
$$\sin\theta$$ = $$\frac{1}{5}$$, where $$\theta=\angle EBF.$$

Find the maximum possible area of rectangle$$ABCD$$ in $$\text{cm}^2.$$

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