To find the total area of the lateral faces of the hexagonal pyramid that will be covered in green paint, we first need to find the total lateral surface area of the pyramid.
Since the hexagonal pyramid is made up of 6 congruent triangular faces, the total lateral surface area of the pyramid is given by:
Total lateral surface area = 6 * Area of one triangular face
Since the base of each triangular face is a side of the hexagon, the area of the base of each triangular face is:
Area of base = (1/2) * Perimeter of hexagon * Height
Area of base = (1/2) * 6 * 15 cm * 20 cm
Area of base = 90 cm * 20 cm
Area of base = 1800 cm squared
Given that the total area of the hexagon is 585 cm squared, we can determine the area of just the hexagonal base:
Area of hexagonal base = 6 * Area of each triangular face - 585 cm squared
6 * 1800 cm squared - 585 cm squared = 10800 cm squared - 585 cm squared = 10215 cm squared
This means that the total lateral surface area of the hexagonal pyramid to be covered in green paint is:
10215 cm squared
So, Byron will be covering 10215 square centimeters with green paint.
Byron made his mother a wood paperweight in the shape of a hexagonal pyramid. He is going to paint the lateral faces of the pyramid green. Each side of the hexagon is 15cm. The height of each triangular face is 20cm and the area of the hexagon is 585 cm squared how many square centimeters will be covered in green paint
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