1.45. In a circle of radius $R$, two parallel chords are drawn on opposite sides of the center, one of which subtends an arc of $60^{\circ}$, the other an arc of $120^{\circ}$. Find the area of the part of the circle enclosed between the chords.
1.45. The area of the segment with an arc of $60^{\circ}$ is $S_{1}=\frac{\pi R^{2}}{6}-\frac{R^{2} \sqrt{3}}{4}$, and the area of the segment with an arc of $120^{\circ}$ is

![](https://cdn.mathpix.com/cropped/2024_05_21_1e3d8d2f6605ac23e2a5g-434.jpg?height=475&width=450&top_left_y=755&top_left_x=690)

Fig. 1.36 $S_{2}=\frac{\pi R^{2}}{3}-\frac{R^{2} \sqrt{3}}{4}$. The desired area is

$$
S=\pi R^{2}-S_{1}-S_{2}=\frac{R^{2}(\pi+\sqrt{3})}{2}
$$

Answer: $0.5 R^{2}(\pi+\sqrt{3})$.