How do I calculate b on a parallelogram given some info?

[Ana.stasia]

The question is:
The surface area of the parallelogram is 36m². The place where the two diagonals are crossed is away from the sides 2m and 3m. What is the sum of all fours sides. I have figured out that a=9.
Here is how:

Just in case of a language barrier. P is surface area, O is the sum of all sides, h is the height. (h_a is the height for the base side, h_b is for the other side)
However no matter how hard I tried, I couldn't get b.
I have googled this problem and I got this:


EF=3 GE=2
HF=6, GI=4
(similar to what I did)

P=a⋅h_a => 36=a⋅6 => a=6
P=b⋅h_b => 36=b⋅4 => b=9

O=2⋅a+2⋅b=2⋅6+2⋅9=12+18=30

Now the result is correct. However I cannot understand how GI is h_b

In school we thought that h_b looks like this:



So can someone please explain to me how and why is the h_b they have drawn equal to this h_b or if it's not and the fact that the solution is correct is accidental. If that is the case please explain to me how I can solve it.

Thank you in advance.

 

[Dr.Peterson]

Any perpendicular segment from AD to BC has the same length, namely h_b.

That includes the altitude shown in the last picture, as well as GI in the previous picture.

The pictures you drew do not show that line being perpendicular to the sides, as it must be.

 

[Ana.stasia]

Any perpendicular segment from AD to BC has the same length, namely h_b.

That includes the altitude shown in the last picture, as well as GI in the previous picture.

The pictures you drew do not show that line being perpendicular to the sides, as it must be.

Thank you so much for the explanation.