A pencil holder shaped like a triangular prism is shoA pencil holder shaped like a triangular prism is shown. The height of the prism is 12 centimeters.
What is the lateral surface area of the pencil holder in square centimeters?wn. The height of the prism is 12 centimeters.
What is the lateral surface area of the pencil holder in square centimeters?
To find the lateral surface area of a triangular prism, we need to calculate the area of each of the three sides and then sum them up.
The formula for the area of a triangle is 1/2 * base * height.
Since the triangular prism has three sides, we need to calculate the area of each triangle and then sum them up.
Let's assume the base of the triangle is b centimeters and the height of the triangle is h centimeters.
The lateral surface area of the triangular prism can be calculated as follows:
Lateral Surface Area = Area of Side 1 + Area of Side 2 + Area of Side 3
Side 1:
The base of this triangle is the height of the prism, which is 12 centimeters, and the height of the triangle is also the height of the prism. So, the area of side 1 is 1/2 * 12 * 12 = 72 square centimeters.
Side 2:
Since the base and height of this triangle are the same as side 1, the area of side 2 is also 72 square centimeters.
Side 3:
The base of this triangle is the same as the height of the prism, which is 12 centimeters, and the height of the triangle is the length of one of the sides of the triangular prism. Since we don't have that length provided, we can't calculate the exact area of side 3.
Therefore, we can only calculate the lateral surface area of the pencil holder if we know the length of one of the sides.