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.
(1 point)
Number of pints of paint=
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To calculate the surface area of the triangular prism, we need to find the area of each face and then add them up.
1. Area of the triangular face (base):
Area = 1/2 * base * perpendicular height
Area = 1/2 * 8 * 6
Area = 24 square inches
2. Area of the other triangular face:
This triangle is congruent to the base triangle since they are opposite faces of the prism. Therefore, the area is also 24 square inches.
3. Area of the three rectangular faces:
Since each of the rectangular faces has the same dimensions, we can focus on calculating the area of one and then multiply by 3.
Area = length * height
Area = 19 * 6
Area = 114 square inches
Now, to find the total surface area of the triangular prism, we sum up the areas of all faces:
Total surface area = 2(24) + 3(114)
Total surface area = 48 + 342
Total surface area = 390 square inches
Since 1 pint of paint covers 200 square inches, we need to calculate how many pints of paint are needed:
Number of pints of paint = Total surface area / Area covered by 1 pint
Number of pints of paint = 390 / 200
Number of pints of paint = 1.95
Since paint is only sold in whole pints, the skateboard club will need to purchase 2 pints of paint.