The figure consists of 8 identical small parallelograms, joined as shown. Including these 8 small parallelograms, how many parallelograms appear in this figure?
(A) 29
(B) 30
(C) 26
(D) 27
(E) 28

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-026.jpg?height=225&width=496&top_left_y=695&top_left_x=1226)
The figure formed by combining a pair of adjacent small parallelograms, is also a parallelogram.

For example, each of the two figures shown is a parallelogram. The reason for this is that opposite sides of these new figures are equal in length and they are parallel. We use the notation $a \times b$ to mean that the new figure has $a$ rows of the small

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-111.jpg?height=187&width=314&top_left_y=243&top_left_x=1469)
parallelograms and $b$ columns of the small parallelograms.

Similarly, more than 2 small parallelograms can be combined to form new parallelograms.

In addition to the small parallelogram $(1 \times 1)$ and the $1 \times 2$ and $2 \times 1$ parallelograms shown above, the sizes of the remaining parallelograms that appear in the figure are shown below.
![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-111.jpg?height=194&width=1494&top_left_y=714&top_left_x=324)

In the table below, the number of parallelograms of each of the different sizes is shown.

| Size | $1 \times 1$ | $1 \times 2$ | $2 \times 1$ | $1 \times 3$ | $1 \times 4$ | $2 \times 2$ | $2 \times 3$ | $2 \times 4$ |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| Number of Parallelograms | 8 | 6 | 4 | 4 | 2 | 3 | 2 | 1 |

The number of parallelograms appearing in the figure is $8+6+4+4+2+3+2+1=30$.

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