Question

You need to create a decorative box to gift your friend a pyraminx. The pyraminx is a triangular pyramid made of 4 equilateral triangles. You want your decorative box to hold that same shape and fit tightly around the pyraminx. How much material do you need to cover each of the four sides?

Answer 1

- The box must hold the same shape as the pyramix and be tight around it. This means that the box must have a surface area equal to that of the pyramix.

- This simply means we need to find the surface area of the pyramid shape of the pyramix.

- To do this, we simply need to find the area of one triangular face and multiply by 4 since there are 4 faces.

- The area of an equilateral triangle is:

`\begin{gathered} A=(√(3))/(4)x^2 \\ where, \\ x=\text{ the length of a side} \end{gathered}`

- We know the length of a triangle in the pyramid is 3.75, thus, the amount of material needed to cover each of the 4 sides is:

`A=(√(3))/(4)*3.75^2=6.089in^2`

- Each of the 4 sides need to be covered by 6.089 square inches of material