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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.

(1 point)
Number of pints of paint=
Remaining Attempts : 3

1 answer

To determine the number of pints of paint needed, we first need to calculate the surface area of the 3D triangular prism.

Step 1: Calculate the surface area of the triangular prism.

  1. Area of the triangular face: The formula for the area \( A \) of a right triangle is: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] Here, the base is 8 inches and the height is 6 inches. \[ A = \frac{1}{2} \times 8 \times 6 = 24 \text{ square inches} \]

  2. Area of the two triangular faces: Since there are two triangular faces, we multiply the area by 2: \[ \text{Area of two triangular faces} = 2 \times 24 = 48 \text{ square inches} \]

  3. Area of the rectangular faces: The prism has three rectangular faces. The dimensions of these rectangles are:

    • The rectangle parallel to the base of the triangle:
      • Area = base × length = \(8 \times 19 = 152\) square inches
    • The rectangle parallel to the height of the triangle:
      • Area = height × length = \(6 \times 19 = 114\) square inches
    • The rectangle parallel to the hypotenuse of the triangle:
      • Area = hypotenuse × length = \(10 \times 19 = 190\) square inches

    Adding these areas gives: \[ \text{Area of three rectangular faces} = 152 + 114 + 190 = 456 \text{ square inches} \]

  4. Total surface area: Finally, we sum the areas of the triangular and rectangular faces: \[ \text{Total surface area} = \text{Area of two triangular faces} + \text{Area of three rectangular faces} \] \[ \text{Total surface area} = 48 + 456 = 504 \text{ square inches} \]

Step 2: Calculate the number of pints of paint required.

Given that one pint of paint covers 200 square inches, we can determine the number of pints needed: \[ \text{Number of pints} = \frac{\text{Total surface area}}{\text{Coverage per pint}} = \frac{504}{200} = 2.52 \]

Since paint can only be purchased in whole pints, we round up to the nearest whole number. Thus, the skateboard club will need to purchase: \[ \text{Number of pints of paint} = 3 \]

So, the answer is:

Number of pints of paint = 3