Question

Find the area of a parallelogram if the angle between two of the sides is 120° and the two sides are 15 inches and 12 inches

Answer 1

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,

`\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}`

Answer: The area of a parallelogram is,

`A=90\sqrt[]{3}\text{ square inches OR }155.885\text{ square inches}`