Math Help - Area Of A Parellelogram

1. Area Of A Parellelogram

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)

2. Originally Posted by Rimas
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)
the answer is C, A = xysin(0)

Hint:

for parallelogram,
Area = base * height

can you get it now?

3. Could you expand on that answer a little bit more because i thought sin = opposite over hypotenuse but there is no hypotenuse here.

4. Originally Posted by Rimas
Could you expand on that answer a little bit more because i thought sin = opposite over hypotenuse but there is no hypotenuse here.
actually, there is a hypotenuse. on the left side, x is the hypotenuse. maybe a modified diagram will help. can you do it after seeing the following?

Note: the height i mentioned in my previous post is the vertical height

5. Originally Posted by Jhevon
actually, there is a hypotenuse. on the left side, x is the hypotenuse. maybe a modified diagram will help. can you do it after seeing the following?

Note: the height i mentioned in my previous post is the vertical height
So the Sin of (O) = Z/X *(X)*(Y)

6. Originally Posted by Godfather
So the Sin of (O) = Z/X *(X)*(Y)
um, no. sine = opp/hyp

so sin(o) = z/x

7. Originally Posted by Jhevon
um, no. sine = opp/hyp

so sin(o) = z/x
So u get Z/X but what does that do for u

8. Originally Posted by Godfather
So u get Z/X but what does that do for u
ok, here it is:

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)