Answer:
Check attachment for solution
Step-by-step explanation
1. For the first aspect,
We want to design, the area using exactly six pieces i.e. Pieces = 6
We should not that, the triangle at the edges are fixed, the cannot be replaced by rectangle
So, we have three triangle. So we are going to use the triangle at the edges.
Now we need to design the rectangle(required) which is 3 by 4 with three rectangle ( from the give shapes) so that it can complete using 6 pieces
We can use the horizontal 1 unit by 4 unit, we will make it vertical, so we need three of that to make it 3 by 4 as required by the area.
So, check attachment for better understanding
2. For the second aspect
We don't want the pieces to get to 6, i.e. pieces ≠ 6
Same as above, the triangle are fixed, so we already have 3 triangle,
So we need to design the rectangle (required) with less than 3 shapes
The required rectangle is 3 by 4
So, if we picked the 3 by 2 rectangle, it is in vertical direction, then, we rotate it to horizontal position, and we will need two of it to make it 3 by 4 .
So the total shape used is 5, then we used 5pieces here.
