10
9
Squares are actually also rectangles so you could make 8 rectangles without touching any of the squares. However, if you could cut the squares, that would be a different problem....
To determine how many rectangles of different sizes can be formed from 36 identical squares, we first need to find the possible dimensions of rectangles that can be created using these squares. The total area of the rectangles must equal 36, which can be expressed as ( length \times width = 36 ). The pairs of factors of 36 are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6), leading to 10 unique rectangles when considering both orientations (length × width and width × length). Thus, a total of 10 different rectangles can be formed.
There are infinitely many such rectangles.
As many as there are different rectangles.
10
3
9
You can make three rectangles. Remember that a square can also be a rectangle.5x14x23x3
Assuming the 12 squares are the same size, three. And three more if you count different orientations (swapping length and breadth) as different rectangles.
13
Infinite amounts.
There are many different quadrilaterals such as squares, trapezoids, rectangles, rhombus and parallelogram.
No not all rectangles are similar because the proportions are different.
3 or 6, depending on whether rectangles rotated through 90 degrees are counted as different. The rectangles are 1x12, 2x6 3x4 and their rotated versions: 4x3, 6x2 and 12x1.
Squares are actually also rectangles so you could make 8 rectangles without touching any of the squares. However, if you could cut the squares, that would be a different problem....