Given:
The angle between two of the sides of the parallelogram is 120°.
The two sides are 15 inches and 12 inches.
The area of the parallelogram is calculated as,
[tex]\begin{gathered} A=ab\sin \theta \\ A=12\cdot15\cdot\sin 120^{\circ} \\ \sin 120^{\circ}=\cos (90^{\circ}-120^{\circ})=\cos (-30^{\circ})=\frac{\sqrt[]{3}}{2} \\ A=180\cdot\frac{\sqrt[]{3}}{2} \\ A=90\sqrt[]{3} \end{gathered}[/tex]
Answer: The area of a parallelogram is,
[tex]A=90\sqrt[]{3}\text{ square inches OR }155.885\text{ square inches}[/tex]
