To determine how many pints of paint the skateboard club needs to purchase, we first need to calculate the surface area of the triangular prism.
Step 1: Surface Area Calculation
The surface area \( A \) of a triangular prism can be calculated using the formula:
\[ A = 2B + Ph \]
where \( B \) is the area of the triangular base, \( P \) is the perimeter of the base, and \( h \) is the height (length) of the prism.
Base Area \( B \): Since the triangular face is a right triangle, the area \( B \) can be calculated using the formula:
\[ B = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 6 = 24 \text{ square inches} \]
Perimeter \( P \): The perimeter of the triangular base is the sum of the lengths of its sides.
- The lengths of the sides:
- base: \( 8 \) inches
- height: \( 6 \) inches
- hypotenuse: \( 10 \) inches
\[ P = 8 + 6 + 10 = 24 \text{ inches} \]
Height of the prism \( h \): Given as \( 19 \) inches.
Step 2: Calculate the Surface Area \( A \):
Now we can substitute our calculated values into the surface area formula:
\[ A = 2B + Ph \] \[ A = 2(24) + (24)(19) \] \[ A = 48 + 456 \] \[ A = 504 \text{ square inches} \]
Step 3: Calculate the Number of Pints of Paint Required
Since one pint of paint covers \( 200 \) square inches, we can find the number of pints required by dividing the total surface area by the coverage per pint:
\[ \text{Number of pints} = \frac{A}{200} = \frac{504}{200} = 2.52 \]
Since paint is sold only in whole pints, we will round up to the nearest whole number:
\[ \text{Number of pints of paint} = 3 \]
Final Answer
The skateboard club needs to purchase 3 pints of paint.