He measured the height of the box to be 3 in. Then, Stephan drew a line from the center of one of the hexagons to each of its vertices and noticed that all the triangles he created have a height of 5 in and a base of 6 in.
Based on this information, we can assume that each side of the hexagon is also 6 inches long (since the base of each triangle is one side of the hexagon).
To find the area of one hexagon, we can use the formula:
Area = (3√3)/2 x s^2
where s = length of one side of the hexagon.
Plugging in s = 6, we get:
Area = (3√3)/2 x 6^2
Area = (3√3)/2 x 36
Area = 54√3
So the area of one hexagon is 54√3 square inches.
To find the volume of the box, we multiply the area of one hexagon by the height of the box:
Volume = 54√3 x 3
Volume = 162√3 cubic inches.
Therefore, the volume of the box is 162√3 cubic inches.
It seems like you have described a geometric situation involving a box and hexagons. To better understand the situation, let's break it down step by step:
Step 1: Measuring the height of the box
- Stephan measured the height of the box and found it to be 3 inches.
Step 2: Drawing lines from the center of a hexagon to its vertices
- Stephan drew a line from the center of one of the hexagons to each of its vertices.
Step 3: Observing the triangles created
- By drawing those lines, Stephan created several triangles.
Step 4: Properties of the triangles
- Stephan noticed that all the triangles he created have a height of 5 inches and a base of 6 inches.
Please let me know if there are any specific questions you have or if you would like more information about any of the steps mentioned above.