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Trenton is building a skateboarding ramp in the shape of a triangular prism. According to his plan, the ramp would have a base of 2 feet, a height of 1.5 feet, and a length of 3 feet. The riding surface would measure 2.5 feet.   If Trenton wants to cover all faces of the ramp with plywood, how much plywood will he need to buy?

Respuesta :

Answer:

The answer is 21 square feet of plywood.

Step-by-step explanation:

Answer:

Trenton needs 21 square feet of plywood to cover all the surface of the ramp.

Step-by-step explanation:

Givens

  • Base is 2 feet long.
  • Height is 1.5 feet long.
  • Length is 3 feet long.
  • The riding surface is 2.5 feet long.

Notice that the ramp is formed by two triangles and three rectangles.

Each triangle has a base of 2 feet and a height of 1.5 feet. So, the area of each triangle is

[tex]A_{triangle}=\frac{bh}{2}=\frac{2(1.5)}{2}=1.5ft^{2}[/tex]

The base of the ramp has dimensions of 3 feet x 2 feet. Its are is

[tex]A_{base}=3(2)=6ft^{2}[/tex]

The back of the ram has an area of

[tex]A_{back}=1.5(3)=4.5 ft^{2}[/tex]

The riding surface is

[tex]A_{riding}=3(2.5)= 7.5ft^{2}[/tex]

So, basically, to know the total surface, we just have to sum the are of both triangles, and the area of all three rectangles, as follows

[tex]S=1.5+1.5+6+4.5+7.5=21ft^{2}[/tex]

This means that Trenton needs 21 square feet of plywood to cover all the surface of the ramp.