Question

1 look at the first model it. why might you choose to divide the logo into triangles and a parallelogram? 2 look at the expression in the second model it. the product 6·5 represents the area of the rectangle. what does the product 2·(1/2·3·3) represent? why is this product subtracted from the area of the rectangle? 3 what is the area of the logo? how is the strategy of adding to find the area related to the strategy of subtracting to find the area? how are these strategies similar and different? 4 how can you find the area of a polygon when you do not know a formula for the area of that polygon? 5 reflect think about all the models and strategies you have discussed. describe how one of them helped you better understand how to find the area of a polygon.

Explanation:

Step1: Analyze polygon - division

Dividing a polygon into triangles and parallelograms simplifies area - calculation as we know the area formulas for these basic shapes.

Step2: Analyze rectangle - related products

The product \(6\times5\) likely represents the area of a rectangle with length 6 and width 5. The product \(2\times(\frac{1}{2}\times3\times3)\) represents the combined area of two right - angled triangles (since the area of a triangle is \(\frac{1}{2}bh\)) that are being subtracted from the rectangle's area to find the area of a more complex shape.

Step3: Area of the logo

To find the area of the logo, we can use either the addition or subtraction strategy. The addition strategy involves breaking the logo into smaller, known - shape pieces (like triangles and rectangles) and adding their areas. The subtraction strategy involves enclosing the logo in a larger shape (like a rectangle) and subtracting the areas of the non - logo parts (like triangles).

Step4: Area of an unknown - formula polygon

When we don't know the area formula for a polygon, we can divide it into triangles, rectangles, parallelograms, etc. whose area formulas we know, and then find the sum or difference of their areas.

Step5: Reflect on models and strategies

For example, the division into triangles strategy helps because any polygon can be decomposed into triangles. Once we find the area of each triangle, we can sum them up to get the area of the whole polygon.

Answer:

1. Divide into basic shapes for easy area - calculation.
2. \(6\times5\) is rectangle area, \(2\times(\frac{1}{2}\times3\times3)\) is combined triangle area for subtraction.
3. Use addition or subtraction of known - shape areas.
4. Decompose into known - formula shapes.
5. Division into triangles helps in finding polygon area by summing triangle areas.