Question

Use the image to answer the question.An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measure 19 inches and 8 inches. The perpendicular side of the triangular face measures 6 inches and the hypotenuse measures 10 inches. The diagram represents a model of a ramp the skateboard club wants to create at the neighborhood skate park. If one pint of paint covers 200 square inches, how many pints of paint will the club need to purchase? Paint is only sold in whole pints.

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, we need to calculate the surface area of the triangular prism. The total surface area of a triangular prism can be calculated by adding the areas of the two triangular faces and the three rectangular faces.

Area of the triangular faces:
1/2 * base * height = 1/2 * 8 * 6 = 24 square inches (each)

Area of the rectangular faces:
(2 * base * length) + (base * height) = (2 * 8 * 19) + (8 * 6) = 304 square inches + 48 square inches = 352 square inches (total)

Therefore, the total surface area of the triangular prism is 24 + 24 + 352 = 400 square inches.

To determine how many pints of paint are needed, we divide the total surface area by 200 square inches per pint:
400 / 200 = 2 pints

Therefore, the skateboard club will need to purchase 2 pints of paint for the ramp.

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

I made an error in my calculations. Let me try again.

The total surface area of the triangular prism can be calculated as follows:

Area of the two triangular faces:
2 * (1/2 * base * height) = 2 * (1/2 * 8 * 6) = 48 square inches

Area of the three rectangular faces:
2 * (base * length) + (base * height) = 2 * (8 * 19) + (8 * 6) = 304 + 48 = 352 square inches

Total surface area = 48 + 352 = 400 square inches

To determine how many pints of paint are needed, we divide the total surface area by 200 square inches per pint:

400 / 200 = 2 pints

Therefore, the skateboard club will need to purchase 2 pints of paint for the ramp.