A pencil holder shaped like a triangular prism is shown. The height of the prism is 12 centimeters, base 7, and width 10.
What is the lateral surface area of the pencil holder in square centimeters?
The lateral surface area of a triangular prism can be calculated by finding the perimeter of the base and multiplying it by the height of the prism.
To find the perimeter of the triangular base, we first need to find the length of one side of the triangle.
Since the base of the triangular prism is 7 centimeters and the width is 10 centimeters, we can use the Pythagorean theorem to find the length of one side of the triangle.
Let the length of one side of the triangle be x.
Using the Pythagorean theorem:
x^2 + 7^2 = 10^2
x^2 + 49 = 100
x^2 = 100 - 49
x^2 = 51
x = √51 ≈ 7.14
The perimeter of the triangular base is 3 times the length of one side:
Perimeter = 3 * 7.14 ≈ 21.43
Now we can calculate the lateral surface area:
Lateral Surface Area = Perimeter of the base * Height
Lateral Surface Area = 21.43 * 12
Lateral Surface Area ≈ 257.16
Therefore, the lateral surface area of the pencil holder is approximately 257.16 square centimeters.