The formula to calculate the Number of Rectangles is:
\[ \text{NRectangles} = C(\text{NHorizontal Lines}+1, 2) \times C(\text{NVertical Lines}+1, 2) \]
The Number of Rectangles is the total count of rectangles that can be formed by using a given set of horizontal and vertical lines from a plane. Number of Horizontal Lines is the total count of given straight lines which are horizontally oriented on a plane. Number of Vertical Lines is the total count of given straight lines which are vertically oriented on a plane.
Let's assume the following values:
Using the formula:
\[ \text{NRectangles} = C(10+1, 2) \times C(9+1, 2) = \frac{11 \cdot 10}{2} \times \frac{10 \cdot 9}{2} = 2475 \]
The Number of Rectangles is 2475.
| Number of Horizontal Lines | Number of Vertical Lines | Number of Rectangles |
|---|---|---|
| 1 | 1 | 1 |
| 1 | 2 | 3 |
| 1 | 3 | 6 |
| 1 | 4 | 10 |
| 1 | 5 | 15 |
| 1 | 6 | 21 |
| 1 | 7 | 28 |
| 1 | 8 | 36 |
| 1 | 9 | 45 |
| 1 | 10 | 55 |
| 2 | 1 | 3 |
| 2 | 2 | 9 |
| 2 | 3 | 18 |
| 2 | 4 | 30 |
| 2 | 5 | 45 |
| 2 | 6 | 63 |
| 2 | 7 | 84 |
| 2 | 8 | 108 |
| 2 | 9 | 135 |
| 2 | 10 | 165 |
| 3 | 1 | 6 |
| 3 | 2 | 18 |
| 3 | 3 | 36 |
| 3 | 4 | 60 |
| 3 | 5 | 90 |
| 3 | 6 | 126 |
| 3 | 7 | 168 |
| 3 | 8 | 216 |
| 3 | 9 | 270 |
| 3 | 10 | 330 |
| 4 | 1 | 10 |
| 4 | 2 | 30 |
| 4 | 3 | 60 |
| 4 | 4 | 100 |
| 4 | 5 | 150 |
| 4 | 6 | 210 |
| 4 | 7 | 280 |
| 4 | 8 | 360 |
| 4 | 9 | 450 |
| 4 | 10 | 550 |
| 5 | 1 | 15 |
| 5 | 2 | 45 |
| 5 | 3 | 90 |
| 5 | 4 | 150 |
| 5 | 5 | 225 |
| 5 | 6 | 315 |
| 5 | 7 | 420 |
| 5 | 8 | 540 |
| 5 | 9 | 675 |
| 5 | 10 | 825 |
| 6 | 1 | 21 |
| 6 | 2 | 63 |
| 6 | 3 | 126 |
| 6 | 4 | 210 |
| 6 | 5 | 315 |
| 6 | 6 | 441 |
| 6 | 7 | 588 |
| 6 | 8 | 756 |
| 6 | 9 | 945 |
| 6 | 10 | 1,155 |
| 7 | 1 | 28 |
| 7 | 2 | 84 |
| 7 | 3 | 168 |
| 7 | 4 | 280 |
| 7 | 5 | 420 |
| 7 | 6 | 588 |
| 7 | 7 | 784 |
| 7 | 8 | 1,008 |
| 7 | 9 | 1,260 |
| 7 | 10 | 1,540 |
| 8 | 1 | 36 |
| 8 | 2 | 108 |
| 8 | 3 | 216 |
| 8 | 4 | 360 |
| 8 | 5 | 540 |
| 8 | 6 | 756 |
| 8 | 7 | 1,008 |
| 8 | 8 | 1,296 |
| 8 | 9 | 1,620 |
| 8 | 10 | 1,980 |
| 9 | 1 | 45 |
| 9 | 2 | 135 |
| 9 | 3 | 270 |
| 9 | 4 | 450 |
| 9 | 5 | 675 |
| 9 | 6 | 945 |
| 9 | 7 | 1,260 |
| 9 | 8 | 1,620 |
| 9 | 9 | 2,025 |
| 9 | 10 | 2,475 |
| 10 | 1 | 55 |
| 10 | 2 | 165 |
| 10 | 3 | 330 |
| 10 | 4 | 550 |
| 10 | 5 | 825 |
| 10 | 6 | 1,155 |
| 10 | 7 | 1,540 |
| 10 | 8 | 1,980 |
| 10 | 9 | 2,475 |
| 10 | 10 | 3,025 |