Chocolate bliss makes a candy bar in the shape of a triangle prism. The prism is represented by the net given for packing the top and the bottom are covered in gold foil and the faces are covered in red foil how many centimeters squared of red foil are needed for the candy bar.
1056cm^2
720cm^2
816cm^2
960cm^2
To calculate the total surface area covered in red foil, we need to find the area of each face of the triangle prism.
The net of the triangle prism consists of 2 equilateral triangles (top and bottom) with side length 12 cm and 3 rectangles (the lateral faces) with dimensions 12cm by 28cm.
Area of each equilateral triangle = √3/4 * side^2
Area of each equilateral triangle = √3/4 * 12^2
Area of each equilateral triangle = √3/4 * 144
Area of each equilateral triangle = 18√3
Area of each rectangle = length * width
Area of each rectangle = 12 * 28
Area of each rectangle = 336
Total area of red foil required = 2 * (18√3) + 3 * 336
Total area of red foil required = 36√3 + 1008
Total area of red foil required ≈ 1058cm^2
Therefore, the correct answer is 1056cm^2.