A pencil holder shaped like a triangular prism is shown. The height of the prism is 12 centimeters.
10 cm
12 cm
7 cm
7 cm
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 base and multiply it by the height.
The base of the prism is a triangle, and we know the height is 12 cm.
To find the perimeter of the base, we need to add up the lengths of all three sides of the triangle:
10 cm + 12 cm + 7 cm = 29 cm.
Now we can find the lateral surface area:
Lateral surface area = perimeter of base * height
Lateral surface area = 29 cm * 12 cm
Lateral surface area = 348 cm^2.
The lateral surface area of the pencil holder is 348 square centimeters.