Use the image to answer the question.
An illustration shows a solid triangular prism with length 15 centimeters, width 6 centimeters, perpendicular height of the triangular face 5.77 centimeters, and side of triangular face 6.5 centimeters.
What is the total surface area of the pencil sharpener? Your answer should have two decimal places.
To find the total surface area of the pencil sharpener, we need to calculate the areas of all the individual surfaces and then add them together.
The triangular prism has two triangular faces and three rectangular faces.
1. The area of each triangular face can be calculated using the formula: Area = 1/2 * base * height.
For the triangular face with a base of 6.5 centimeters and a height of 5.77 centimeters, the area is:
Area_triangular = 1/2 * 6.5 cm * 5.77 cm = 18.8225 cm^2
2. The area of each rectangular face can be calculated using the formula: Area = length * width.
For the rectangular faces, we have two faces with dimensions 15 cm x 6 cm and one face with dimensions 6.5 cm x 5.77 cm.
Area_rectangular1 = 15 cm * 6 cm = 90 cm^2
Area_rectangular2 = 15 cm * 6 cm = 90 cm^2
Area_rectangular3 = 6.5 cm * 5.77 cm = 37.605 cm^2
Now, we can calculate the total surface area by adding up all the individual areas:
Total surface area = 2 * Area_triangular + 3 * (Area_rectangular1 + Area_rectangular2 + Area_rectangular3)
Total surface area = 2 * 18.8225 cm^2 + 3 * (90 cm^2 + 90 cm^2 + 37.605 cm^2)
Total surface area = 2 * 18.8225 cm^2 + 3 * 217.605 cm^2
Total surface area = 37.645 cm^2 + 652.815 cm^2
Total surface area = 690.46 cm^2
Therefore, the total surface area of the pencil sharpener is 690.46 square centimeters.
The total surface area of the pencil sharpener can be calculated by finding the area of each of its faces and adding them together.
There are two triangular faces and three rectangular faces.
The area of each triangular face can be found using the formula:
Area = (1/2)*base*height
For the triangular face with base 6.5 cm and height 5.77 cm, the area is:
Area = (1/2)*6.5 cm*5.77 cm = 18.76 cm²
So the total area of both triangular faces is:
2*18.76 cm² = 37.52 cm²
The area of each rectangular face can be found using the formula:
Area = length*width
For the rectangular face with length 15 cm and width 6 cm, the area is:
Area = 15 cm*6 cm = 90 cm²
And for the two rectangular faces with length 5.77 cm and width 6 cm, the area of each is:
Area = 5.77 cm*6 cm = 34.62 cm²
So the total area of all three rectangular faces is:
2*34.62 cm² + 90 cm² = 159.24 cm²
Adding the area of the triangular faces and the area of the rectangular faces together gives us:
37.52 cm² + 159.24 cm² = 196.76 cm²
Therefore, the total surface area of the pencil sharpener is 196.76 cm².