Calculate the lateral surface area of a regular quadrangular prism, the diagonal

Calculate the lateral surface area of a regular quadrangular prism, the diagonal is 12√3 cm and is inclined to the base plane at an angle of 30 degrees.

So, to solve this problem, we must clearly understand what a correct 4-angle prism is.

If it is really correct, it means that there is a square at its base.

So let’s start deciding.

If 1 angle = 30 °, then this means that the other angle will be = 1/2 * 1 angle.

Hence, 2 angle = 6 * √3.

Now, by the Pythagorean theorem, we can also establish that the next side = 18.

And since we have a square at the base, the area of the lateral side = 72 * √6.