# Thread: find area of parallelogram

1. ## find area of parallelogram

I was wondering if someone could check my work I am not getting the same answer that is in the back of the book. The question is to find the area of a parallelogram if the two sides measure 8.4 inches and 3.4 inches and one angle measures 135 degrees.

I tried using both the pythagorean theorem and the law of cosines and still couldn't come up with the correct answer, but the answer key in the book has been known to have typo's.

I'd appreciate any help, thanks

2. ## Re: find area of parallelogram

I get $\displaystyle \left( {3.4} \right)\left( {8.4} \right)\sin \left( {{{45}^o}} \right) = 20.1950$

3. ## Re: find area of parallelogram

Never mind I discovered my mistake!

4. ## Re: find area of parallelogram

what formula is that? is that just half of the law of cosines? I ended up drawing my picture wrong, which is the majority of my application problem mistakes

5. ## Re: find area of parallelogram

The area of a parallelogram is "base times height". You can take either of the two sides as "base" but then the height is measured perpendicular to that base. Here, taking the "3.4" side as base, drawing a perpendicular from the other vertex to that side, we have a right triangle with hypotenuse of length 8.4 and angle 180- 135= 45 degrees. sin(45)= "opposite side over hypotenuse" so that height= "opposite side" times sin(45)= 8.4 sin(45). Therefore the area of the parallelogram is (3.4)(8.4) sin(45).