[ Area of a quadrilateral ]

The area of a quadrilateral is 3 cm², and the lengths of its diagonals are 6 cm and 2 cm. Find the angle between the diagonals.

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The area of a quadrilateral is equal to half the product of its diagonals by the sine of the angle between them, i.e., $\frac{1}{2} \cdot 6 \cdot 2 \cdot \sin \alpha = 3$, from which we find that $\sin \alpha = \frac{1}{2}$. Since $\alpha < 90^{\circ}$ (the angle between lines), then $\alpha = 30^{\circ}$.

## Answer

$30^{\circ}$.