After learning about the egyptians, Mr paint'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 in and a height of 10.4 in the three sides will be isosceles triangles measuring 10 inches by 10 in x 12 in with an 8-in 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, we first calculate the area of each triangle and then add them together.
Area of the equilateral triangle base:
Area = (sqrt(3)/4) * s^2
Area = (sqrt(3)/4) * 12^2
Area = (sqrt(3)/4) * 144
Area = 36sqrt(3)
Area of one isosceles triangle:
Area = (1/2) * base * height
Area = (1/2) * 10 * 8
Area = 40
Total paper needed:
36sqrt(3) + 3(40)
36sqrt(3) + 120
≈ 184.392 inches squared
Therefore, Riley's group will need approximately 184.392 square inches of butcher paper to construct their pyramid.