We must find the amount of cardboard needed to make a slice of pizza box which basically means finding the surface area of the piece of box shown. This is composed of five faces divided in three groups:
- Two equal triangular faces with a base of 6.7 in and a height of 11 in.
- Two equal rectangular faces with a base of 11.5 in and a height of 1 in.
- A single rectangular face with a base of 6.7 in and a height of 1 in.
The area of the piece of box is given by the sum of the areas of the 5 faces so let's find the area of the faces of each group.
The area of a triangle is given by half the product of the length of its base and its height. Then the area of each triangular face is:
[tex]A_t=\frac{6.7\times11}{2}=36.85[/tex]So each triangular face has an area of 36.85 in².
The area of a rectangle is given by the product of its base and height. Then for the pair of equal rectangular faces we have:
[tex]A_{r1}=11.5\times1=11.5[/tex]So each of these two faces has an area of 11.5 in².
The area of the remaining rectangular face is then given by:
[tex]A_{r2}=6.7\times1=6.7[/tex]So the area of the last face is 6.7 in².
Then the total surface area is given by the sum of the areas of the 5 faces. Then we get:
[tex]A=2A_t+2A_{r1}+A_{r2}=2\times36.85+2\times11.5+6.7=103.4[/tex]AnswerThen the answer is 103.4
