MHB What is the area of a parallelogram without knowing the height?

[jljarrett18]

I am working on a task right now. I am currently trying to find the area of a parallelogram. I do not have the height. I only have the dimensions. I have tried suggestions like dividing the parallelogram into triangles and doing 1/2bh. The dimensions I have are the 1/2,1/2,\sqrt{2}/4, \sqrt{2}/4. I have attached a picture of what I am working on. View attachment 2736

 

[Prove It]

I am working on a task right now. I am currently trying to find the area of a parallelogram. I do not have the height. I only have the dimensions. I have tried suggestions like dividing the parallelogram into triangles and doing 1/2bh. The dimensions I have are the 1/2,1/2,\sqrt{2}/4, \sqrt{2}/4. I have attached a picture of what I am working on. View attachment 2736

Do you have any of the angles?

 

[jljarrett18]

Do you have any of the angles?

Yes, Angle E and K are 45 degrees, and angles h and g are 135 degrees.

 

[Prove It]

Yes, Angle E and K are 45 degrees, and angles h and g are 135 degrees.

OK since you have the lengths of two non-parallel sides of the parallelogram (call them "a" and "b") and the angle between them (call it "C") you can find the area using $\displaystyle \begin{align*} A = a\,b\sin{(C)} \end{align*}$.

 

[jljarrett18]

My parallelogram has two pairs of parallel sides so which sides am I using?

 

[Prove It]

My parallelogram has two pairs of parallel sides so which sides am I using?

I said use two non-parallel lengths of the parallelogram and the angle between them.

 

[jljarrett18]

So I would do A= (1/2)(√2/4)Sin(135) ?

 

[Prove It]

So I would do A= (1/2)(√2/4)Sin(135) ?

Yes you could do that. You could also do $\displaystyle \begin{align*} \frac{1}{2}\cdot \frac{\sqrt{2}}{4} \cdot \sin{ \left( 45^{ \circ} \right) } \end{align*}$ :)

 

[Opalg]

So I would do A= (1/2)(√2/4)Sin(135) ?

Alternatively, you could use the fact that the area of a parallelogram is the length of one side times the perpendicular distance between that side and the opposite side. In this case, the length of the vertical sides is $\frac12$, and the perpendicular distance between them is $\frac14$.

 

[jljarrett18]

So the answer would be 1/8?

 

[Prove It]

So the answer would be 1/8?

1/8 of a square unit, yes :)

 

[jljarrett18]

Thank you!