# Mario's father is building a skateboard ramp in the shape of a triangular prism. Part A The surface area of the ramp, not including the bottom, is 504 square feet. Find the length of the sloped surface of the ramp, x.

Marios
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SoosteethicU
Since the bottom of the ramp is not included in the surface area, find the surface area of the ramp by finding the areas of the faces.
The ramp has a rectangular face with dimensions of xx ft by 10.5 ft on top so the area of this face is 10.5x square feet.
The ramp has a rectangular face with dimensions of 10.5 ft by 7 ft in the back so the area of this face is 10.5(7)=73. square feet.
The ramp also has two triangular faces with bases of 24 ft and heights of 7 ft so the area of each of these triangular faces is 12(24)(7)=12(7)=84 square feet.
The surface area of the ramp is then 10.5x+73.5+2(84) square feet. Since the surface area of the ramp is 504 square feet, then:
10.5x+73.5+2(84)=504
10.5x+73.5+168=504
10.5x+241.5=504
10.5x=262.5
x=25
The length of the sloped surface of the ramp is then x=25 ft