The Area Of A Parallelogram can be given in terms of the lengths x and y of two adjacent sides and a trigonometric function of the angle formed by those two sides. Which of the following formulas gives the area A of this parallelogram and why?
A. A=xy cos(o)
B. A=xy tan(o)
C. A=xy sin(o)
D. A=xy cot(o)
see diagram below.
let the vertical height be z.
for a parallelogram, A = height*base
remember, the height is z, but we have:
sin(o) = z/x
=> z = xsin(0) ........this is the formula for the vertical height.
the base is y
so, A = height*base = y * xsin(0) = xysin(0)