 In this problem we have to calculate the second moment of area, or moment of inertia, for the following section. So, we can calculate this using different approaches or methods. For example, one of them would be calculating the moment of inertia of this smaller rectangle containing this section and subtracting the moment of inertia of this hollow part. What I propose instead is to calculate the moment of inertia of the flange first, the upper one and the lower one, and the moment of inertia of the web, and sum them up. Then, in order to calculate the moment of inertia, first we need to locate our coordinate reference system. But in this case it's pretty simple because since we have this double symmetric section we know that the neutral axis is located exactly at 50 mm from the bottom surface of the beam. Then this is my coordinate reference system as you can see here in this figure. Then I can start calculating for example the moment of inertia of the web We know that for a rectangular section the moment of inertia is equal to b h cubed divided by 12. So, in this case this is my web. Then the moment of inertia with respect to the z-axis is equal to, as I said before, 112 b times h squared which is this equal to 1 divided by 12 times 10 mm times 80 to the power of 3. And this is equal to 4.267 times 10 to the power of positive 5. Now we can calculate the moment of inertia of the flange. We can start for instance with the upper one. Then the moment of inertia of this section with respect to this axis is equal to 1 over 12 times b h squared. So this is equal to 1 over 12 times 150. This is the base times 10 to the power of 3. But remember that we do not want to calculate the moment of inertia with respect to this axis, but with respect to this axis. Then we can use the parallel axis theorem. This theorem basically says that we can translate the moment of inertia of the section with respect to one axis to another axis which is parallel to the first one. Then in this case we have basically that the moment of inertia with respect to 1 which is the coordinate reference system of the problem. It is equal to the moment of inertia with respect to 2 plus a d squared. So what is a? a is the area of the section. In this case we calculated the moment of inertia of this section. So this is a and d is the distance between the axis. Then in this case we have that. Then this is the moment of inertia of the upper flange. And now we need to calculate the moment of inertia of the second flange of this one. But we have symmetry of course. Then in this case the moment of inertia of the second flange is exactly the same. Then the total moment of inertia is equal to the moment of inertia of the web plus 2 times the moment of inertia of the flange. Then this is equal to...