Horizontal and vertical area moment of inertia

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Please see the attached file.

Find the horizontal and vertical area moment of inertias of the cross-section shown with respect to its centroid.
b1 = 55.0mm
b2 = 20.0mm
b3 = 32.0mm
r1 = 0.0mm
r2 = 20.0mm
r3 = 80.0mm
r4 = 100.0mm

Please show all work.

Solution:
Step 1) find all the necessary lengths as follows

Step 2) locate the coordinate axis
In this case, the problem says "vertical and horizontal".

Then divide the total area into small parts of which ...