How do I find the area of this parallelogram? (lateral side 9cm, bases 12cm, angle 73*)

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chijioke

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To find the area of the parallelogram below,
IMG_20230417_125510.jpg
this is what I would do:
IMG_20230417_130841.jpg
Again, to find the area of another parallelogram,IMG_20230417_125510.jpg
this is another thing I would do:
IMG_20230417_131324.jpg
I am continuing in post #2.
 

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I continue. But what if I am given this parallelogramIMG_20230417_135749.jpg
I would not know how to find the area because the height or included is is not given. Do you have any clue as to how to go about it?
 
chijioke said:
I continue. But what if I am given this parallelogramView attachment 35579
I would not know how to find the area because the height or included is is not given. Do you have any clue as to how to go about it?
Click to expand...
Come on, you need to try something. Can you label the angles? Which ones are congruent?
 
Angle DAB is congruent to angle DCB and angle ADC is congruent to angle ABC . So what next?
 
chijioke said:
Angle DAB is congruent to angle DCB and angle ADC is congruent to angle ABC . So what next?
Click to expand...
Label that in your diagram. What do all the angles add up to? Are there any lines that you can draw to help?
 
Steven G said:
Great! Go for it.
Do you know the sum of any other angles?
Click to expand...
As it concerns the problem at hand. I don't.
Steven G said:
Have you tried using the side that measures 1.5cm.
Click to expand...
I know that the area of a parallelogram is = base × height. But I am not seeing that side which measures as 1.5cm as the height.
Steven G said:
Keep going you can do this or confirm that you can't find the area.
Click to expand...
If I want to try, I would say the area is [math]1. 5 cm × 18cm= 27 cm^2[/math] But I am doubting my solution because I am not sure if 1.5 cm is the height.
 
chijioke said:
If I want to try, I would say the area is [math]1. 5 cm × 18cm= 27 cm^2[/math] But I am doubting my solution because I am not sure if 1.5 cm is the height.
Click to expand...
It can't be "\(\displaystyle 27 cm^2\)" or it would be a rectangle!
 
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chijioke said:
Yes. You are right! Thanks for coming to the rescue. It seems Steven G is no where to be found now.
Click to expand...
Like the Terminator, he will be back (when it suits him ?).
(As I suggested (in private) he may just be "teasing" the "correct" answer out of you;
@Steven G likes to make people work for their dinner. ?)
 
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Of course you have to work for your dinner/solution.
I just want the student to know everything about the problem so they could find the are or conclude that there is no solution.
Yes, you do know the sum of two pair of angles. What is the sum and how does that help you?
 
If you move triangle BCE to the other side you get the figure on the right (with the same area)...

Paralellogram.jpg


but it's simply not possible to calculate the area of a parallelogram knowing only the side lengths but no internal angle's measure.

1681954072095.png
 
Look at how much information you failed to list. It is reasonable to assume that with this missed information you could have solved the problem.
Adjacent angles in a parallelogram are supplementary!

IMG_1494.jpg
 
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