A. The rectangular grid in figure 4.1 has a length of 3 units and a width of 2 units. Thus its area is 3×2=6 square units.

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$$\begin{gathered} In figure 4.1 area of the rec\tan gle is 3\times 2=6 sq. units \\ A paticular area can have multiple dimensions if we vary the lengths and breadths accordingly \\ Here, factors of 6=1, 2, 3, 6 \\ so, rectangles having area (6 sq. units)having integral dimension would be \\ 1\times 6, 2\times 3, 3\times 2 and 6\times 1 \\ in figure 4.2 area of the rectangle is 6\times 1=6 sq. units \\ so, area of 4.1 and 4.2 are same \\ and we can get two more rectangular grid with the same area. i.e. 2\times 3 and 1\times 6 \\ . \\ now, given area is 36 sq. units \\ here, factors of 36=1, 2, 3, 4, 6, 9, 12, 18, 36 \\ So, possible rectangular grids would be \\ 1\times 36 \\ 2\times 18 \\ 3\times 12 \\ 4\times 9 \\ 6\times 6 \\ 9\times 4 \\ 12\times 3 \\ 18\times 2 \\ 36\times 1 \\ so, 9 types of rectangular grids are possible. \end{gathered}$$
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