1x16
2x8
and 4x4
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Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. So, there are 5 rectangles with an area of 36 cm^2 is 5.
The area of a rectangle is worked out by the equation axb when a is length and b is width. Thus, if a and b are both integers, a good way to work out possible lengths would be to break down the area into its prime factors. These are 2, 3 and 3. Now any product of these primes for a, and the other prime for b, will work as a possible rectangle. For example a=2x3=6 and b=3 will work a=3x3=9 and b=2 will work Thus possible rectangles are 1x18, 2x9 and 3x6
Rectangles don't have height. They have length and width, one value for each. The area is the product of those two values.
You can't tell the area from knowing the perimeter. There are an infinite number of different rectangles, all with the same perimeter, that all have different areas. Here are a few rectangles that all have perimeters of 42. The last number after each one is its area: 1 cm by 20 cm . . . . . 20 square centimeters 2 x 19 . . . . . 38 3 x 18 . . . . . 54 4 x 17 . . . . . 68 5 x 16 . . . . . 80 10 x 11 . . . 110
A triangular prism.