On a scale drawing of the front of a square earring, each side of the square is 3.2cm. The scale from the earring to the drawing is 4mm to 2cm. What is the area of the front of the actual earring?

The scale provided is 4 mm (on the drawing) to 2 cm (on the actual earring). This means the ratio of the drawing size to the actual size is \( \frac{4 \text{ mm}}{2 \text{ cm}} \).

First, convert the 4 mm into cm:

\[
4 \text{ mm} = 0.4 \text{ cm}
\]

Thus, the scale becomes:

\[
\frac{0.4 \text{ cm}}{2 \text{ cm}} = \frac{1}{5}
\]

This means that the dimensions of the drawing are 5 times smaller than the actual dimensions of the earring. 

Next, the side length of the square in the drawing is 3.2 cm. To find the side length of the actual earring, multiply this by 5:

\[
\text{Side length of the actual earring} = 3.2 \text{ cm} \times 5 = 16 \text{ cm}
\]

Now, to find the area of the actual earring (which is a square), use the formula for the area of a square:

\[
\text{Area} = \text{side length}^2 = 16 \text{ cm} \times 16 \text{ cm} = 256 \text{ cm}^2
\]

Thus, the area of the front of the actual earring is \( 256 \, \text{cm}^2 \).

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. How do you calculate the perimeter of a square if you know its side length?
2. What is the scale factor if the scale were 1 cm on the drawing to 5 cm on the actual object?
3. How does the area change if the scale changes to 1:10?
4. How would you calculate the area of an earring if it was a circle instead of a square?
5. What is the importance of maintaining consistent units when calculating areas and scales?

**Tip**: Always ensure that the units used in your calculations match the problem's context to avoid errors.

Find the area of an actual square earring using a scale factor. The drawing shows a square with sides of 3.2 cm and a scale of 4mm to 2cm. Learn how to calculate the area with key concepts like scale factor and area of a square. Suitable for Grades 6-8.

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