Question
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.
(1 point)
in.2
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.
(1 point)
in.2
Answers
GPT 3.5
The total surface area of the triangular prism can be calculated using the formula:
Total Surface Area = 2*(Area of triangular face) + (Perimeter of triangular face)*length of prism
First, we find the area of the triangular face:
Area = (1/2)*base*height
Area = (1/2)*1.5*1.12
Area = 0.84 in^2
Next, we find the perimeter of the triangular face:
Perimeter = 3*side
Perimeter = 3*1.5
Perimeter = 4.5 inches
Now, we can calculate the total surface area of the prism:
Total Surface Area = 2*(0.84) + (4.5)*6
Total Surface Area = 1.68 + 27
Total Surface Area = 28.68 in^2
Therefore, the total surface area of this eraser is 28.68 in^2.
Total Surface Area = 2*(Area of triangular face) + (Perimeter of triangular face)*length of prism
First, we find the area of the triangular face:
Area = (1/2)*base*height
Area = (1/2)*1.5*1.12
Area = 0.84 in^2
Next, we find the perimeter of the triangular face:
Perimeter = 3*side
Perimeter = 3*1.5
Perimeter = 4.5 inches
Now, we can calculate the total surface area of the prism:
Total Surface Area = 2*(0.84) + (4.5)*6
Total Surface Area = 1.68 + 27
Total Surface Area = 28.68 in^2
Therefore, the total surface area of this eraser is 28.68 in^2.
not it
GPT 3.5
My apologies for the error. Let's correct the calculation:
The total surface area of the triangular prism can be calculated as follows:
Each triangular face has an area of (1/2) * base * height
Area of a triangular face = (1/2) * 1.5 * 1.12 = 0.84 sq in
The lateral surface area (the three rectangular faces) can be calculated by summing the areas of the three rectangles:
Lateral Surface Area = (perimeter of the triangular face) * (height of the prism)
Lateral Surface Area = 3 * 1.5 * 6 = 27 sq in
Adding the two areas together, we get the total surface area:
Total Surface Area = 2 * 0.84 + 27
Total Surface Area = 1.68 + 27
Total Surface Area = 28.68 sq in
Therefore, the total surface area of this eraser is 28.68 sq in.
The total surface area of the triangular prism can be calculated as follows:
Each triangular face has an area of (1/2) * base * height
Area of a triangular face = (1/2) * 1.5 * 1.12 = 0.84 sq in
The lateral surface area (the three rectangular faces) can be calculated by summing the areas of the three rectangles:
Lateral Surface Area = (perimeter of the triangular face) * (height of the prism)
Lateral Surface Area = 3 * 1.5 * 6 = 27 sq in
Adding the two areas together, we get the total surface area:
Total Surface Area = 2 * 0.84 + 27
Total Surface Area = 1.68 + 27
Total Surface Area = 28.68 sq in
Therefore, the total surface area of this eraser is 28.68 sq in.