A pencil holder shaped like a triangular prism is shown. The height of the prism is 12 centimeters while the base is 10, 7, and 7. What is the lateral surface area of the pencil holder in square centimeters?
To find the lateral surface area of the triangular prism, we need to find the perimeter of the triangular base and multiply it by the height of the prism.
The perimeter of the triangular base can be found by adding the lengths of the three sides.
Perimeter = 10 + 7 + 7 = 24 cm
The lateral surface area is then the perimeter multiplied by the height of the prism.
Lateral Surface Area = Perimeter × Height = 24 cm × 12 cm = 288 square cm
Therefore, the lateral surface area of the pencil holder is 288 square centimeters.