A pencil holder shaped like a triangular prism is shown. The height of the prism is 12 cm what is the lateral surface area of the square centimeters
To find the lateral surface area of a triangular prism, we need to find the perimeter of the base and multiply it by the height of the prism.
Since the base of the prism is a triangular shape, let's find the perimeter of the base first. If the height is 12 cm, we can divide it by 3 to find the height of one of the triangular faces.
12 cm / 3 = 4 cm
Now, we can assume that the triangular prism is an equilateral triangle. If one side of the equilateral triangle is 4 cm, we can multiply it by 3 to find the perimeter.
4 cm * 3 = 12 cm
Now, we can find the lateral surface area by multiplying the perimeter by the height of the prism.
12 cm * 12 cm = <<12*12=144>>144 cm²
Therefore, the lateral surface area of the pencil holder is 144 square centimeters.