.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.
To find the surface area of the triangular prism, we need to find the area of each of the three faces (two triangular faces and one rectangular face) and add them together.
1. The area of the triangular face:
Area = 0.5 * base * perpendicular height
Area = 0.5 * 8 * 6
Area = 24 square inches
2. The area of the rectangular face:
Area = base * length
Area = 8 * 19
Area = 152 square inches
3. The area of the other triangular face will be the same as the first one, 24 square inches.
Now, we add all three areas together:
24 + 152 + 24 = 200 square inches
Since 1 pint of paint covers 200 square inches, the skateboard club will need to purchase 1 pint of paint to cover the entire surface area of the triangular prism ramp.