Moments of inertia using parallel axis theorem

[TheRedDevil18]

Homework Statement

The mass of a homogenous thin plate is 36kg. Determine it moment of inertia about the x axis

Homework Equations

Parallel axis theorem:
Ix = Ix' + d^2*m

The Attempt at a Solution

p = m/a
= 36/0.36 = 100

Because the density is homogenous, I found the mass of the first rectangle:
m = pa
= 100*0.24
= 24kg

Ix = Ix' + d^2*m (MOI for the first rectangle)
= 1/12*b*h^3 + d^2*m
= 1/12(0.4)(0.6)^3 + (0.3)^2(24)
= 2.1672

Ix = Ix' + d^2*m (MOI for the second rectangle)
= 1/12*b*h^3 + d^2*m
= 1/12(0.4)(0.3)^3 + (0.15)^2(12).....Mass of second rectangle = 36-24 = 12
= 0.27

Therefore MOI of the whole object = (MOI for the first rectangle) + (MOI for the second rectangle)
= 2.44

Problem is my textbook gives a total different answer which is 3.24. Please help, I am so confused

 

[Orodruin]

1/12*b*h^3 + d^2*m

This expression does not make sense since the two terms have different units (the first has unit length^4 and the second mass*length^2). I believe you are missing an insertion of the density in the first term.

 

[TheRedDevil18]

Oh yes, sorry. That should have been 1/12*m*h^2 + d^2*m. It now works out to 3.24. I mistakenly used the area moment of inertia formula instead of the mass moment of inertia formula. Thanks, :)