ANSWER
A = 48√3 m²
EXPLANATION
Triangle GJH is equilateral, so each side has the same length:
To find the area of the parallelogram we have to find the height, which is the same as the height of the triangle.
We can find H by dividing the triangle into two right triangles as shown above, and applying the Pythagorean theorem:
[tex]8^2=H^2+4^2[/tex]
Solving for H:
[tex]\begin{gathered} H=\sqrt[]{8^2-4^2} \\ H=\sqrt[]{64-16} \\ H=\sqrt[]{48} \\ H=4\sqrt[]{3}m \end{gathered}[/tex]
The area of a parallelogram is:
[tex]A=B\cdot H=EH\cdot H=12\cdot4\sqrt[]{3}=48\sqrt[]{3}m^2[/tex]
