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.
To find the total paper needed for Riley's group to construct their pyramid, we first need to calculate the area of each side of the pyramid.
For the equilateral triangle base:
Area = (sqrt(3) / 4) * s^2
Area = (sqrt(3) / 4) * 12^2
Area = (1.732 / 4) * 144
Area = 41.57 square inches
For the isosceles triangle sides:
Area = (1/2) * base * height
Area = (1/2) * 10 * 8
Area = 40 square inches
Since there are three isosceles triangle sides, the total paper needed for the sides is:
Total area for sides = 3 * 40 = 120 square inches
Now, we add the area of the base and the sides to find the total paper needed:
Total paper needed = Area of base + Total area for sides
Total paper needed = 41.57 + 120
Total paper needed = 161.57 square inches
Therefore, Riley's group will need a total of 161.57 square inches of butcher paper to construct their pyramid.