Height of a parallelogram

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gbloyer

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Hello, all. I'm trying to help my daughter who has Geometry in high school. I've had to relearn a lot! We're unable to understand how to get the height, which according to the answer sheet, is 4. Another student helped her but unfortunately she didn't make sure she understood the reason. All she wrote down was 8*10=80. I know this would be the area of the shape if you draw a line down the top right corner of the parallelogram (b*h). Then they wrote 80=20*h. Solving for h is 4, but we don't understand how 80 is also the area of the shape containing h. Please help me understand what I'm missing. Thank you in advance.
 
Think only of the parallelogram (not the triangle outside).
[MATH][/MATH]When turned the way it is, the base of the parallelogram is 10 and the perpendicular height is 8.
The area is base [MATH]\times[/MATH] perpendicular height, so it is 80.
Now if you turn the parallelogram around so the long side is the base, then [MATH]h[/MATH] will be the perpendicular height, so the area of the parallelogram is 20 [MATH]\times[/MATH] h.
The parallelogram has only one area, no matter how it is calculated, so [MATH]20h [/MATH] must equal 80 and [MATH]h=4[/MATH].
 
gbloyer said:
View attachment 26484
Hello, all. I'm trying to help my daughter who has Geometry in high school. I've had to relearn a lot! We're unable to understand how to get the height, which according to the answer sheet, is 4. Another student helped her but unfortunately she didn't make sure she understood the reason. All she wrote down was 8*10=80. I know this would be the area of the shape if you draw a line down the top right corner of the parallelogram (b*h). Then they wrote 80=20*h. Solving for h is 4, but we don't understand how 80 is also the area of the shape containing h. Please help me understand what I'm missing. Thank you in advance.
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Another way:

In the figure, there are two similar right triangles with hypotenuses of 20 and 10. the corresponding heights of those triangles are 8 and 'h'.
 
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