Use the image to answer the question.
An illustration shows a triangular prism with length 6 inches, width 2 inches, perpendicular height of the triangular face 1.12 inches, and side of triangular face 1.5 inches.
What is the total surface area of this eraser? Your answer should have two decimal places.
The total surface area can be calculated by adding the areas of all its faces. There are two triangular faces and three rectangular faces.
The area of one triangular face is (1/2) x base x height, where the base is 1.5 inches and the height is 1.12 inches.
Area of one triangular face = (1/2) x 1.5 x 1.12 = 0.84 square inches
The area of one rectangular face is length x width.
Area of one rectangular face = 6 x 2 = 12 square inches
Therefore, the total surface area is:
2 x 0.84 + 3 x 12 = 25.68 square inches
Rounded to two decimal places, the total surface area is 25.68 square inches.
it says incorrect :(
I apologize for the mistake. Let's check the calculations again.
The area of one triangular face is (1/2) x base x height, where the base is 1.5 inches and the height is 1.12 inches.
Area of one triangular face = (1/2) x 1.5 x 1.12 = 0.84 square inches
The area of one rectangular face is length x width.
Area of one rectangular face = 6 x 2 = 12 square inches
To calculate the total surface area of the prism, we need to add the areas of all five faces.
Total surface area = 2 x area of triangular face + 3 x area of rectangular face
Total surface area = 2 x 0.84 + 3 x 12
Total surface area = 25.68 square inches
Therefore, the total surface area of the eraser is 25.68 square inches.
To find the total surface area of the triangular prism eraser, we need to calculate the areas of all its faces and then add them together.
First, let's identify the different faces of the triangular prism:
1. Rectangular Base: The triangular prism has two rectangular bases, each with dimensions 6 inches by 2 inches. The area of each rectangular base is 6 * 2 = 12 square inches. Since there are two bases, we multiply this by 2 to get a total of 12 * 2 = 24 square inches.
2. Lateral Faces: The triangular prism has three lateral faces, each of which is a rectangle with dimensions 6 inches by 1.5 inches. To find the area of each lateral face, we multiply these dimensions: 6 * 1.5 = 9 square inches. Since there are three lateral faces, we multiply this by 3 to get a total of 9 * 3 = 27 square inches.
3. Triangular Faces: The triangular prism has two triangular faces, each with a base of 1.5 inches and a perpendicular height of 1.12 inches. To find the area of each triangular face, we multiply the base by the height and then divide it by 2: (1.5 * 1.12) / 2 = 0.84 square inches. Since there are two triangular faces, we multiply this by 2 to get a total of 0.84 * 2 = 1.68 square inches.
Now, let's calculate the total surface area by adding up the areas of all the faces:
Rectangular Base: 24 square inches
Lateral Faces: 27 square inches
Triangular Faces: 1.68 square inches
Total Surface Area = 24 + 27 + 1.68 = 52.68 square inches
Therefore, the total surface area of the triangular prism eraser is 52.68 square inches.