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