Question

After learning about the Egyptians Mr Pink's class wants to create their own pyramids with triangular bases. Each group needs to create their measurements and identify how much but your paper they will need to construct their pyramid before they can start Riley's group has determined that they want to have an equilateral triangle base of 12 in and a height of 10.4 in with an 8-in height. How many total paper will Riley's group need to construct repairman? Write your answer in decimal form.

Answer 1

To calculate the total paper needed for Riley's group to construct their pyramid, we first need to determine the total surface area of the pyramid.

The formula for the surface area of a triangular pyramid is:

Surface Area = base area + (1/2 x base perimeter x slant height)

In this case, the base of the pyramid is an equilateral triangle with side length 12 inches. We can calculate the area using the formula for the area of an equilateral triangle:

Base Area = (sqrt(3) / 4) x side^2
Base Area = (sqrt(3) / 4) x 12^2
Base Area = (1.732 / 4) x 144
Base Area = 41.569 in^2

The perimeter of the base triangle is 3 times the side length:

Base Perimeter = 3 x 12
Base Perimeter = 36 in

The slant height of the pyramid is the height of the pyramid, which is given as 10.4 inches.

Now we can calculate the surface area of the pyramid:

Surface Area = 41.569 + (1/2 x 36 x 10.4)
Surface Area = 41.569 + (1/2 x 36 x 10.4)
Surface Area = 41.569 + 187.2
Surface Area = 228.769 in^2

Each sheet of paper is typically 8.5 x 11 inches, which gives a total area of 93.5 in^2.

To find out how many sheets of paper Riley's group will need, we divide the total surface area of the pyramid by the area of one sheet of paper:

Total Paper = Surface Area / Paper Area
Total Paper = 228.769 / 93.5
Total Paper ≈ 2.45 sheets of paper

Therefore, Riley's group will need approximately 2.45 sheets of paper to construct their pyramid.