Finding the area of non-standard polygons missing measurements

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How do you find the area of non-standard polygons missing a few measurements?
Here's a replica of a polygon i had to find the area of on my 9th grade final exam.

enter image description here

I understand the fact you have to turn this mess into a bunch of known shapes then find out the area of each of them.

The problem is, how am i supposed to find the missing width or height of the sides colored in red on the drawing below if it doesn't even look like anything i already have the measurements of?

enter image description here