Question

scaling squares
for problems 2–7, use the provided scale factors to create a scale drawing of each
then calculate the areas of the original figure and the scale drawing.

problem	original figure	scale factor	scale drawing	area of the original figure
3.	(1x1 square on grid)	3	(grid)
4.	(1x1 square on grid)	4	(grid)

Explanation:

To solve the problem of finding the areas of the original square and its scale drawing, we follow these steps for each problem (2, 3, and 4):

Problem 2:

Step 1: Area of Original Figure

The original square has a side length of \( 1 \) unit. The area of a square is \( \text{side length}^2 \).
\[
\text{Area}_{\text{original}} = 1^2 = 1 \text{ square unit}
\]

Step 2: Side Length of Scale Drawing

The scale factor is \( 2 \). The new side length is \( \text{original side length} \times \text{scale factor} \).
\[
\text{New side length} = 1 \times 2 = 2 \text{ units}
\]

Step 3: Area of Scale Drawing

Using the new side length, calculate the area.
\[
\text{Area}_{\text{scale}} = 2^2 = 4 \text{ square units}
\]

Problem 3:

Step 1: Area of Original Figure

The original square has a side length of \( 1 \) unit.
\[
\text{Area}_{\text{original}} = 1^2 = 1 \text{ square unit}
\]

Step 2: Side Length of Scale Drawing

Scale factor is \( 3 \).
\[
\text{New side length} = 1 \times 3 = 3 \text{ units}
\]

Step 3: Area of Scale Drawing

\[
\text{Area}_{\text{scale}} = 3^2 = 9 \text{ square units}
\]

Problem 4:

Step 1: Area of Original Figure

The original square has a side length of \( 1 \) unit.
\[
\text{Area}_{\text{original}} = 1^2 = 1 \text{ square unit}
\]

Step 2: Side Length of Scale Drawing

Scale factor is \( 4 \).
\[
\text{New side length} = 1 \times 4 = 4 \text{ units}
\]

Step 3: Area of Scale Drawing

\[
\text{Area}_{\text{scale}} = 4^2 = 16 \text{ square units}
\]

Summary of Results:

Problem	Original Area	Scale Drawing Area
3	\( 1 \)	\( 9 \)
4	\( 1 \)	\( 16 \)

(Note: For the scale drawing, you would draw a square with side length equal to the original side length multiplied by the scale factor. For example, in Problem 2, draw a square with side length \( 2 \) units.)

Answer:

To solve the problem of finding the areas of the original square and its scale drawing, we follow these steps for each problem (2, 3, and 4):

Problem 2:

Step 1: Area of Original Figure

The original square has a side length of \( 1 \) unit. The area of a square is \( \text{side length}^2 \).
\[
\text{Area}_{\text{original}} = 1^2 = 1 \text{ square unit}
\]

Step 2: Side Length of Scale Drawing

The scale factor is \( 2 \). The new side length is \( \text{original side length} \times \text{scale factor} \).
\[
\text{New side length} = 1 \times 2 = 2 \text{ units}
\]

Step 3: Area of Scale Drawing

Using the new side length, calculate the area.
\[
\text{Area}_{\text{scale}} = 2^2 = 4 \text{ square units}
\]

Problem 3:

Step 1: Area of Original Figure

The original square has a side length of \( 1 \) unit.
\[
\text{Area}_{\text{original}} = 1^2 = 1 \text{ square unit}
\]

Step 2: Side Length of Scale Drawing

Scale factor is \( 3 \).
\[
\text{New side length} = 1 \times 3 = 3 \text{ units}
\]

Step 3: Area of Scale Drawing

\[
\text{Area}_{\text{scale}} = 3^2 = 9 \text{ square units}
\]

Problem 4:

Step 1: Area of Original Figure

The original square has a side length of \( 1 \) unit.
\[
\text{Area}_{\text{original}} = 1^2 = 1 \text{ square unit}
\]

Step 2: Side Length of Scale Drawing

Scale factor is \( 4 \).
\[
\text{New side length} = 1 \times 4 = 4 \text{ units}
\]

Step 3: Area of Scale Drawing

\[
\text{Area}_{\text{scale}} = 4^2 = 16 \text{ square units}
\]

Summary of Results:

Problem	Original Area	Scale Drawing Area
3	\( 1 \)	\( 9 \)
4	\( 1 \)	\( 16 \)

(Note: For the scale drawing, you would draw a square with side length equal to the original side length multiplied by the scale factor. For example, in Problem 2, draw a square with side length \( 2 \) units.)