The total surface area of the pyramid can be calculated by finding the area of each triangular face and adding them up, plus the area of the triangular base.
For the equilateral triangle base:
Area = (sqrt(3)/4) * (side length)^2
Area = (sqrt(3)/4) * (12)^2
Area = (sqrt(3)/4) * 144
Area = 36sqrt(3) square inches
For the three isosceles triangles:
Area = 1/2 * base * height
Area = 1/2 * 10 * 8
Area = 40 square inches each
Total area for the three isosceles triangles:
40 + 40 + 40 = 120 square inches
Total surface area:
36sqrt(3) + 120 = 36sqrt(3) + 120 square inches
Now we need to find the total surface area in decimal form:
36sqrt(3) ≈ 62.3 square inches
Total surface area ≈ 62.3 + 120 ≈ 182.3 square inches
Therefore, Riley's group will need approximately 182.3 square inches of butcher paper to construct their pyramid.
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 butcher 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 inches and a height of 10.4 inches. The three sides will be isosceles triangles measuring 10 inches by 10 inches by 12 inches with an 8-inch height. How much total paper will Riley’s group need to construct their pyramid? Write your answer in decimal form.
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