Question

Find the area of a parallelogram with side lengths of 10 m and 16 m and an angle that measures 120

Answer 1

138.6 square meters

Explanation:

If we do not know the height of the parallelogram, we can use the concept of trigonometry to find its area, like this:

The value of h would be the product of side 10 times the sine of the indicated angle. We find this angle, knowing that the sum of all the internal angles is equal to 360 °, therefore, we calculate it like this:

`\begin{gathered} 360=120+120+x+x \\ \text{ we solve x:} \\ 2x=360-120-120 \\ x=(120)/(2) \\ x=60\text{\degree} \end{gathered}`

Which means, that the area would be:

`\begin{gathered} A=b\cdot h \\ h=10\cdot\sin 60 \\ \text{ replacing} \\ A=16\cdot10\cdot\sin 60 \\ A=138.6m^2 \end{gathered}`

The area is equal to 138.6 square meters