# Find the volume of the hexagonal-shaped plastic box

• MHB
angubk6
A chocolate company produces triangular chocolate bars. The length of the chocolate bar is x cm, and its cross section is an isosceles triangle. The length of the base side of the cross section is 3 cm, the height is h cm, and the two base angles are 50 degrees.
View attachment 9689

Moreover, the company uses a hexagonal-shaped plastic box to pack 24 chocolate bars together as shown in the figure below.
View attachment 9690

What is the volume of the hexagonal-shaped plastic box?

*I would like to apologize if I keep on editing the content of my problem. Originally, the question asked was to find the volume of the hexagonal shaped plastic box. In my opinion, I can only solved this if I will be able to find the volume of each triangular chocolate bars then multiply it by 24 (please correct me if my view was invalid). However, I am really having a hard time in solving for x.

#### Attachments

Last edited:

Gold Member
MHB
Is it asking you for the height of the chocolate bar, or the side length?

Have you drawn a diagram?

skeeter
$h = \dfrac{3}{2}\tan(50^\circ)$

You’ll need the bar’s volume to determine the length of the bar, $x$.

skeeter
*I would like to apologize if I keep on editing the content of my problem. Originally, the question asked was to find the volume of the hexagonal shaped plastic box. In my opinion, I can only solved this if I will be able to find the volume of each triangular chocolate bars then multiply it by 24 (please correct me if my view was invalid). However, I am really having a hard time in solving for x.

What measurement information was given about the hexagonal box? As it sits, there is not enough information to determine $x$.

Gold Member
MHB
*I would like to apologize if I keep on editing the content of my problem. Originally, the question asked was to find the volume of the hexagonal shaped plastic box. In my opinion, I can only solved this if I will be able to find the volume of each triangular chocolate bars then multiply it by 24 (please correct me if my view was invalid). However, I am really having a hard time in solving for x.