Question

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.

Answer 1

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.