An artist makes a scale drawing of a parallelogram-gram shaped sculpture. The scale is 10 cm on the drawing for every 8m on the sculpture. What is the area of the scale drawing? Show your work

To find the area of the scale drawing, we'll first use the scale to find the dimensions of the drawing based on the sculpture's dimensions.

### Step 1: Define the scale
- The scale is given as 10 cm on the drawing for every 8 meters (or 800 cm) on the sculpture.
  
This means the linear dimensions in the drawing are \(\frac{10}{800} = \frac{1}{80}\) of the actual sculpture's dimensions.

### Step 2: Area scaling
- When scaling down dimensions, the area changes by the square of the scale factor. In this case, the scale factor is \(\frac{1}{80}\) for each side.
  
Thus, the area of the drawing will be scaled by:

\[
\left(\frac{1}{80}\right)^2 = \frac{1}{6400}
\]

### Step 3: Area of the scale drawing
- Let \(A\) be the area of the sculpture in square centimeters.
- The area of the drawing will be \(\frac{A}{6400}\) in square centimeters.

However, since the dimensions of the sculpture aren't provided, you'll need those to calculate the exact area of the drawing. 

Would you like to provide the dimensions of the sculpture or ask more details? 

Here are 5 related questions to expand your understanding:
1. What is the formula for the area of a parallelogram?
2. How does the area scale when the length scale changes?
3. What are examples of scale factors in architecture?
4. How would you convert the area of a sculpture from square meters to square centimeters?
5. What is the geometric significance of scaling down shapes?

**Tip:** Always square the scale factor when determining how area changes between similar figures.

Explore how to calculate the area of a scale drawing of a parallelogram-shaped sculpture using given scale ratios and geometric scaling principles. Learn step-by-step with an example. Suitable for Grades 6-8 students learning about scale drawings and geometric scaling in mathematics.

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