Find the area of a rhombus with two sides that form a 120 degree angle, and the length of each side is 9.
In a rhombus, the area can be calculated using the formula:
Area = (d1 * d2) / 2
where d1 and d2 are the lengths of the diagonals of the rhombus.
In this case, since the rhombus has two sides that form a 120 degree angle, the diagonals will be perpendicular to each other and will intersect at a right angle. This means that the diagonals will be equal in length.
Using trigonometry, we can find the length of each diagonal:
sin(120) = (d1 / 2) / 9
sin(120) = d1 / 18
d1 = 18 * sin(120)
d1 = 18 * √3 / 2
d1 = 9√3
Now that we have the length of one diagonal, we can find the area:
Area = (9 * 9√3) / 2
Area = 81√3 / 2
Area = 40.5√3 square units
Therefore, the area of the rhombus is 40.5√3 square units.