Question

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?

Answer 1

The answer is 21 square feet of plywood.

Explanation:

Answer 2

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

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

`A_(triangle)=(bh)/(2)=(2(1.5))/(2)=1.5ft^(2)`

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

`A_(base)=3(2)=6ft^(2)`

The back of the ram has an area of

`A_(back)=1.5(3)=4.5 ft^(2)`

The riding surface is

`A_(riding)=3(2.5)= 7.5ft^(2)`

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

`S=1.5+1.5+6+4.5+7.5=21ft^(2)`

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