Solution
- 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:
[tex]\begin{gathered} A=\frac{\sqrt{3}}{4}x^2 \\ where, \\ x=\text{ the length of a side} \end{gathered}[/tex]
- 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:
[tex]A=\frac{\sqrt{3}}{4}\times3.75^2=6.089in^2[/tex]
- Each of the 4 sides need to be covered by 6.089 square inches of material
