42x25 rectangular roof(one side)

We need to fill this roof with 8x4 plywood pieces.
So, we need about 33 plywood pieces to fill one side roof.
How do I show a possible arrangement of pieces on half of the roof. Make a few cuts. What is the area of the scrap pieces left?

Thanks.

There seems to be no challenge to this. No limit of cuts or waste area. So any solution is ok, there is no statement that says " minimize waste, or minimize the number of cuts."

So lay out the sheets any way you want.

I would do this on graph paper.

Now if you are trying to minimize waste, or minimize the total cuts, it is entirely a different problem.

To show a possible arrangement of the 8x4 plywood pieces on half of the 42x25 rectangular roof, you can follow these steps:

1. Draw a rectangle on graph paper to represent the half of the roof. Mark the dimensions of the roof as 42x25.

2. Divide the length of the roof (25) by the length of the plywood sheet (8) to determine the number of rows needed. In this case, 25 / 8 = 3 with a remainder of 1. This means you can fit 3 full rows and one piece of plywood that needs to be cut.

3. Place three full 8x4 plywood sheets horizontally at the bottom of the roof diagram, leaving a small gap between each sheet to represent the thickness of the plywood.

4. To accommodate the remaining 1-foot section, cut a piece from another 8x4 plywood sheet to fit the remaining space. You might need to cut it into smaller pieces, depending on the shape of the remaining space.

5. Arrange the cut piece(s) above the three full sheets, filling the remaining space in the diagram.

By following these steps, you can create a possible arrangement of the plywood pieces on half of the roof.

As for calculating the area of the scrap pieces left, you would need to determine the dimensions and shape of the cut piece(s) and any waste area. Measure the length and width of the scrap pieces and multiply them to find the area. Add the areas of all the scrap pieces together to get the total area of waste.