Answer
$I=182in^4$
Work Step by Step
We can find the required moment of inertia as follows:
The area of the first rectangle is given as
$A_1=h\cdot b$
$\implies A_1=(3)(1)=3in^2$
The area of the second rectangle is
$A_2=h\cdot b$
$\implies A_2=(1)(8)=8in^2$
The area of the third rectangle is
$A_3=h\cdot b$
$A_3=(8)(1)=8in^2$
Now $I=\Sigma (I+Ad^2y)$
We plug in the known values to obtain:
$I=\frac{1\cdot (3)^3}{12}+3(1.5)+\frac{8(1)^3}{12}+8(0.5)^2+\frac{1(8)^3}{12}+8(4)^2$
This simplifies to:
$I=182in^4$
