Discussion
| Column A | Column B |
| 15 |
The area of Parallelogram ABCD |
| (A) | Column A is larger |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 07/28/2012 13:17
How do you figure what to multiply by to get the area?
Posted: 07/28/2012 14:10
How do you figure out the height with an angle on a parallelogram?
Posted: 08/10/2015 10:58
Reply: what is the formula is angel is given for a rectangle
Posted: 08/01/2012 19:24
Thad, what the problem's solution is trying to teach is that in tests, we may not need to calculate the height. In order to answer the question whether the area of the parallelogram is larger than 15, we only need to logically deduce by taking an extreme of one situation to the other. One extreme is that angle BAD would be a right one, making it a square with area 15. The other extreme would be the angle BAD is a flat or near flat one (180 degrees), making the area of the parallelogram closer to 0. We can conclude that any parallelogram with an angle BAD smaller than 90 degrees would be less in area to the rectangle.
Posted: 08/01/2012 19:34
Thad, now to answer your question. In case you need to do this for other tests.
The area of a parallelogram is just like a rectangle: b * h, h being the height. b = 3, but h is not 5. Instead, h is the sine projection of 5 to the upright axis, or 5 * sin (65 degrees), or 5 * 0.9... which is around 4.5.. This requires a rudimentary knowledge of trigonometry, which is not a requirement for GRE or SAT (they only require algebra, geometry, and arithmetic knowledge.
Hence the area is 3 x 4.5.. or about 13.5.., which is definitely less than 15.
The area of a parallelogram is just like a rectangle: b * h, h being the height. b = 3, but h is not 5. Instead, h is the sine projection of 5 to the upright axis, or 5 * sin (65 degrees), or 5 * 0.9... which is around 4.5.. This requires a rudimentary knowledge of trigonometry, which is not a requirement for GRE or SAT (they only require algebra, geometry, and arithmetic knowledge.
Hence the area is 3 x 4.5.. or about 13.5.., which is definitely less than 15.
Posted: 08/01/2012 22:49
Thanks for the help!
Posted: 08/02/2012 14:09
You are welcome Thad. If you like the app, please show some love and rate it in the App Store.
Posted: 08/25/2014 16:21
If the problem is asking specifically for parallelogram with a 65 degree angle then why should it matter about if it was a rectangle or had a 30 degree angle? I really don't understand why the other two examples are relevant
Posted: 08/25/2014 16:30
Arneshia, the examples in the explanation are there to show that when a rectangle (which is a parallelogram with 90 degree angle) is tilted with narrower angles, the area gets smaller. Once you can visualize it, then you can decide if the area inside the 65-degree parallelogram is larger than, equal to, or smaller than the rectangle's area, which is 15.
Posted: 08/28/2014 16:00
So do we have to take into account other rectangles and squares etc when solving problems like this?
Posted: 08/28/2014 16:30
Arneshia, I am not sure what you are asking. I suggest you look up the thread and read my explanations. I have answered questions for this problem several times, and you would benefit from going through them.
GRE requires that you have a mastery of algebra and geometry.
GRE requires that you have a mastery of algebra and geometry.
Posted: 06/28/2015 11:45
I couldn't get the exact reason why the area of the parallelogram is less than the area of the rectangle of same dimensions