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 surface area of each face and then add them all together.
1. The two triangular faces:
Each triangular face has an area of 0.5 * base * height.
Area = 0.5 * 6.5 * 5.77 = 18.7225 cm² (rounded to four decimal places)
Since there are two triangular faces, total area for both = 2 * 18.7225 = 37.4450 cm²
2. The three rectangular faces:
- Two faces will have a length of 15 cm and width of 6 cm.
Area = 15 * 6 = 90 cm² for each face, so total area for these two = 2 * 90 = 180 cm²
- One face will have a length of 6.5 cm and width of 5.77 cm.
Area = 6.5 * 5.77 = 37.505 cm²
3. Adding all the areas together:
Total Surface Area = 37.4450 + 180 + 37.505 = 255.9500 cm²
Therefore, the total surface area of the pencil sharpener is 255.95 cm².