What is the area of the parallelogram?

Area of the parallelogram is given by:

Area = Base x Height

Base = 8 cm

Height is the perpendicular distance between the base. 6 cm is not the height, but we can use 6 cm and the angle 60 to find the height. See the picture attached with.

The height x is the perpendicular side of the triangle as shown in figure and 6 is the hypotenuse.

So,we can write

cos 60 = x/6
⇒ 
x = 6 * cos 60 = 3 cm

So, now we can write:

Area of parallelogram = 8 x 3 = 24 cm²