This image presents a problem that asks you to draw a $3 \times 7$ square on a grid and calculate its area, while also showing all reasoning. Let's break it down:

1. Understanding the dimensions:

   • The square is described as $3 \times 7$. Since it's called a "square," it likely refers to the area covered by a grid of $3 \times 7$ dots, which forms a rectangle, not a traditional square. The term "square" here is more related to the concept of area.

2. Drawing the rectangle:

   • To draw a $3 \times 7$ rectangle on the grid, you would need to mark 3 units along one side (the height) and 7 units along the other side (the length), using the dots as reference points.

3. Calculating the area:

   • The area $A$ of a rectangle is given by the formula: $A = \text{length} \times \text{width}$ In this case, the length is 7 units, and the width (height) is 3 units. So, the area is: $A = 3 \times 7 = 21 \text{ square units}$

4. Explanation of reasoning:

   • We defined the dimensions based on the given $3 \times 7$ grid and calculated the area by multiplying the two dimensions. The result, 21 square units, represents the number of smaller square units (formed by the grid) within the $3 \times 7$ shape.

Would you like a more detailed explanation or help in visualizing how to draw the $3 \times 7$ rectangle on the grid?

Here are 5 related questions to think about:

1. How would the area change if the dimensions were doubled (i.e., a $6 \times 14$ rectangle)?
2. Can you find the perimeter of the $3 \times 7$ rectangle?
3. How would you calculate the diagonal length of this $3 \times 7$ rectangle using the Pythagorean theorem?
4. What if the shape was a perfect square (equal side lengths), how would the area be different?
5. How does the concept of area apply in three-dimensional shapes (such as cubes)?

Tip: Always double-check your dimensions when working with geometric shapes, as mistaking the length and width can lead to errors in both drawing and calculations!