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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
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1 answer

To find out how many pints of paint the skateboard club needs to purchase, we first need to calculate the surface area of the triangular prism, which consists of two triangular faces and three rectangular faces.

Step 1: Calculate the Area of the Triangular Faces

The base of the triangular face is 8 inches and the height (perpendicular side) is 6 inches.

\[ \text{Area}_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]

\[ \text{Area}_{triangle} = \frac{1}{2} \times 8 \times 6 = 24 \text{ square inches} \]

Since there are two identical triangular faces:

\[ \text{Total Area}_{triangles} = 2 \times 24 = 48 \text{ square inches} \]

Step 2: Calculate the Area of the Rectangular Faces

The prism has three rectangular faces:

  1. One rectangle with a base of 8 inches and a height equal to the length of the prism, which is 19 inches.
  2. Two rectangles with dimensions equal to the hypotenuse (10 inches) and the length (19 inches) and the perpendicular side (6 inches) and the length (19 inches).

Now, calculate the areas:

  1. Area of the base rectangle: \[ \text{Area}_{base} = \text{base} \times \text{length} = 8 \times 19 = 152 \text{ square inches} \]

  2. Area of the first side rectangle (height 10 inches): \[ \text{Area}_{side1} = \text{hypotenuse} \times \text{length} = 10 \times 19 = 190 \text{ square inches} \]

  3. Area of the second side rectangle (height 6 inches): \[ \text{Area}_{side2} = \text{perpendicular side} \times \text{length} = 6 \times 19 = 114 \text{ square inches} \]

Step 3: Total Surface Area of the Prism

Now add up the areas: \[ \text{Total Surface Area} = \text{Total Area}{triangles} + \text{Area}{base} + \text{Area}{side1} + \text{Area}{side2} \] \[ \text{Total Surface Area} = 48 + 152 + 190 + 114 \] \[ \text{Total Surface Area} = 504 \text{ square inches} \]

Step 4: Calculate the Number of Pints of Paint Needed

Since one pint of paint covers 200 square inches, divide the total surface area by the area covered by one pint of paint:

\[ \text{Number of pints} = \frac{\text{Total Surface Area}}{\text{Area per pint}} = \frac{504}{200} = 2.52 \]

Since paint can only be purchased in whole pints, the skateboard club would need to round up to the next whole number.

Final Answer

The skateboard club needs to purchase 3 pints of paint.