The figure below shows a $9\times7$ arrangement of $2\times2$ squares. Alternate squares of the grid are split into two triangles with one of the triangles shaded. Find the area of the shaded region.
[asy]
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fill((0,5)--(1,5)--(1,4)--cycle^^(1,4)--(2,4)--(2,3)--cycle^^(2,3)--(3,3)--(3,2)--cycle^^(3,2)--(4,2)--(4,1)--cycle^^(4,1)--(5,1)--(5,0)--cycle,rgb(.76,.76,.76));
fill((0,7)--(1,7)--(1,6)--cycle^^(1,6)--(2,6)--(2,5)--cycle^^(2,5)--(3,5)--(3,4)--cycle^^(3,4)--(4,4)--(4,3)--cycle^^(4,3)--(5,3)--(5,2)--cycle^^(5,2)--(6,2)--(6,1)--cycle^^(6,1)--(7,1)--(7,0)--cycle,rgb(.76,.76,.76));
fill((2,7)--(3,7)--(3,6)--cycle^^(3,6)--(4,6)--(4,5)--cycle^^(4,5)--(5,5)--(5,4)--cycle^^(5,4)--(6,4)--(6,3)--cycle^^(6,3)--(7,3)--(7,2)--cycle^^(7,2)--(8,2)--(8,1)--cycle^^(8,1)--(9,1)--(9,0)--cycle,rgb(.76,.76,.76));
fill((4,7)--(5,7)--(5,6)--cycle^^(5,6)--(6,6)--(6,5)--cycle^^(6,5)--(7,5)--(7,4)--cycle^^(7,4)--(8,4)--(8,3)--cycle^^(8,3)--(9,3)--(9,2)--cycle,rgb(.76,.76,.76));
fill((6,7)--(7,7)--(7,6)--cycle^^(7,6)--(8,6)--(8,5)--cycle^^(8,5)--(9,5)--(9,4)--cycle,rgb(.76,.76,.76));
fill((8,7)--(9,7)--(9,6)--cycle,rgb(.76,.76,.76));
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draw((0,1)--(1,0)^^(0,3)--(3,0)^^(0,5)--(5,0)^^(0,7)--(7,0)^^(2,7)--(9,0)^^(4,7)--(9,2)^^(6,7)--(9,4)^^(8,7)--(9,6));
[/asy]
1. First, we need to determine the total number of $2 \times 2$ squares in the $9 \times 7$ grid. Each $2 \times 2$ square occupies a $2 \times 2$ area, so we can count how many such squares fit horizontally and vertically.
   - Horizontally: $\left\lfloor \frac{9}{2} \right\rfloor = 4$ squares
   - Vertically: $\left\lfloor \frac{7}{2} \right\rfloor = 3$ squares

   Therefore, the total number of $2 \times 2$ squares is:
   \[
   4 \times 3 = 12
   \]

2. Each $2 \times 2$ square is divided into two triangles, with one of the triangles shaded. The area of one $2 \times 2$ square is:
   \[
   2 \times 2 = 4 \text{ square units}
   \]

3. Since each $2 \times 2$ square is divided into two equal triangles, the area of one triangle (shaded) is:
   \[
   \frac{4}{2} = 2 \text{ square units}
   \]

4. Given that there are 12 such $2 \times 2$ squares, the total area of the shaded regions is:
   \[
   12 \times 2 = 24 \text{ square units}
   \]

The final answer is $\boxed{24}$