1.62. The area of a quadrilateral is $S$. Find the area of the parallelogram whose sides are equal and parallel to the diagonals of the quadrilateral.
1.62. Since $A L \| B O$ and $L B \| A O$ (Fig. 1.49), then $A L B O$ is a parallelogram and, therefore, $S_{\triangle A L B}=S_{\triangle A O B}$. Similarly, we obtain

![](https://cdn.mathpix.com/cropped/2024_05_21_1e3d8d2f6605ac23e2a5g-442.jpg?height=385&width=595&top_left_y=294&top_left_x=560)

Fig. 1.49 $S_{\triangle B M C}=S_{\triangle B O C}, S_{\triangle D C N}=S_{\triangle D O C}, S_{\triangle A P D}=S_{\triangle A O D}$, from which it follows that $S_{L M N P}=2 S$

Answer: $2 S$.