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Mathias has a wooden bike ramp, shown below. He wants to cover the entire ramp with vinyl to protect the wood surfaces. How much vinyl does he need? Show your work.

Mathias has a wooden bike ramp, shown below. He wants to cover the entire ramp with-example-1
User Manojkumar
by
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1 Answer

6 votes

Here are the steps to solve this problem:

1. Find the area of each face of the ramp.

The rectangular base is 2 meters by 1.5 meters, so the area is 2 x 1.5 = 3 square meters.

The triangular side is 0.5 meters by 1.5 meters, so we use the area of a triangle formula: (base x height)/2 = (0.5 x 1.5)/2 = 0.375 square meters

2. Add the areas of the faces together to find the total surface area that needs to be covered.

3 + 0.375 = 3.375 square meters

3. We need an additional amount for overlaps where the vinyl pieces meet. Let's assume a 10% overlap, or 0.338 square meters.

0.338 + 3.375 = 3.713 square meters

So Mathias needs about 3.7 square meters of vinyl to cover his bike ramp.

In summary:

Area of rectangular base = 2 x 1.5 = 3m^2

Area of triangular side = (0.5 x 1.5)/2 = 0.375m^2

Total area = 3 + 0.375 = 3.375 m^2

Additional 10% for overlap = 0.338m^2

Total vinyl needed = 0.338 + 3.375 = 3.713 m^2

User Speigg
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