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

Answer 1

no

Answer 2

wrong

Answer 3

The total surface area of the triangular prism can be calculated by adding the areas of the two triangular faces and the three rectangular faces.

Area of the two triangular faces:
1/2 * base * height = 1/2 * 1.5 * 1.12 = 0.84 in^2 (for each triangular face)

Area of the three rectangular faces:
2 * (length * width) + 2 * (width * height) + 2 * (length * height) = 2 * (6 * 2) + 2 * (2 * 1.12) + 2 * (6 * 1.12) = 24 + 4.48 + 13.44 = 41.92 in^2

Total surface area = 2 * 0.84 + 41.92 = 3.36 + 41.92 = 45.28 in^2

Therefore, the total surface area of this eraser is 45.28 in^2.

Answer 4

I apologize for the mistake in my previous calculations. Let's reevaluate:

Area of the two triangular faces:
1/2 * base * height = 1/2 * 1.5 * 1.12 = 0.84 in^2 (for each triangular face)

Area of the three rectangular faces:
2 * (length * width) + 2 * (width * height) + 2 * (length * height)
2 * (6 * 2) + 2 * (2 * 1.12) + 2 * (6 * 1.12)
= 24 + 4.48 + 13.44
= 41.92 in^2

Total surface area = 2 * 0.84 + 41.92
= 1.68 + 41.92
= 43.60 in^2

Therefore, the total surface area of this eraser is 43.60 in^2. Thank you for your patience.

Answer 5

Let's reevaluate the calculations:

Area of the two triangular faces:
2 * (1/2 * base * height) = 2 * (1/2 * 1.5 * 1.12) = 2 * 0.84 = 1.68 in^2

Area of the three rectangular faces:
2 * (length * width) + 2 * (width * height) + 2 * (length * height)
= 2 * (6 * 2) + 2 * (2 * 1.12) + 2 * (6 * 1.12)
= 2 * 12 + 2 * 2.24 + 2 * 6.72
= 24 + 4.48 + 13.44
= 41.92 in^2

Total surface area = 1.68 + 41.92
= 43.60 in^2

Therefore, the correct total surface area of the eraser is 43.60 in^2. Thank you for your patience.