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.(1 point) in.2
To calculate the total paper needed for Riley's group pyramid, we need to find the surface area of each of the four triangles that make up the pyramid and add them together.
For the equilateral triangle base:
Surface area = 1/2 x base x height
Surface area = 1/2 x 12 inches x 10.4 inches
Surface area = 62.4 square inches
For the three isosceles triangles:
Surface area = 1/2 x base x height
Surface area = 1/2 x 10 inches x 8 inches
Surface area = 40 square inches
Total paper needed = 4 x (62.4 square inches + 40 square inches)
Total paper needed = 4 x (102.4 square inches)
Total paper needed = 409.6 square inches
Therefore, Riley's group will need 409.6 square inches of butcher paper to construct their pyramid.