Question

quiz
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what is the area of the entire grid?
answer
26
5 numeric 10 points
next, take the 5 darkly shaded cells from the top of the grid and place them on the side of the grid as shown.
now find the total area of the new 5 × 7 grid that you have created.
answer
35
6 essay 10 points
compare your answers for problems 4 and 5. what do you notice about the differences in the areas of the grids? can you write a number sentence that represents this situation?

Explanation:

When moving the 5 darkly - shaded cells, the total number of cells (area) remains the same. The area of a rectangle is calculated as \(A = l\times w\). For the first grid (assuming it's \(5\times7\) as the second one is also \(5\times7\)), the area is \(5\times7=35\). The initial answer of 26 is incorrect. The key point is that moving the cells (a form of translation in geometry) does not change the total area of the grid. A number sentence could be \(5\times7=(5\times7)\) (showing the equality of areas before and after the cell - moving operation).

Answer:

The area of both grids (the original and the new one) is the same. A number sentence is \(5\times7 = 5\times7\) (assuming the original grid is also \(5\times7\)). If we assume there was a mis - count in the first answer (26 is wrong), the correct area for both grids (using the formula for the area of a rectangle \(A = l\times w\) where \(l = 7\) and \(w = 5\)) is \(35\). So, the difference in areas (when the first answer is corrected) is \(0\), and the number sentence is \(35-35 = 0\).