A quadrilateral P is enlarged by a scale factor of 1.2 to give quadrilateral Q. The area of quadrilateral P is 20 cm2. Calculate the area of quadrilateral Q

To calculate the area of quadrilateral \( Q \), we use the relationship between the scale factor and the area. When a shape is enlarged or reduced, the area of the new shape is proportional to the square of the scale factor.

### Step-by-step solution:
1. **Given data**:
   - The scale factor is \( 1.2 \).
   - The area of quadrilateral \( P \) is \( 20 \, \text{cm}^2 \).

2. **Relationship between areas and scale factor**:
   The area of the enlarged shape \( Q \) is related to the area of the original shape \( P \) by the formula:
   \[
   \text{Area of } Q = \text{Area of } P \times (\text{scale factor})^2
   \]

3. **Substitute the values**:
   \[
   \text{Area of } Q = 20 \, \text{cm}^2 \times (1.2)^2
   \]
   \[
   \text{Area of } Q = 20 \, \text{cm}^2 \times 1.44
   \]
   \[
   \text{Area of } Q = 28.8 \, \text{cm}^2
   \]

Thus, the area of quadrilateral \( Q \) is \( 28.8 \, \text{cm}^2 \).

Would you like more details or have any questions about this process?

Here are some related questions to expand your understanding:
1. What would be the area of quadrilateral \( Q \) if the scale factor was 1.5 instead of 1.2?
2. How does the perimeter of a shape change when it's enlarged by a scale factor?
3. If the area of quadrilateral \( P \) were \( 30 \, \text{cm}^2 \), what would the area of \( Q \) be with the same scale factor of 1.2?
4. What happens to the area if the shape is reduced by a scale factor less than 1?
5. Can you explain how the volume of a 3D shape changes with a given scale factor?

**Tip**: Always remember that area scales with the square of the scale factor, while perimeter scales linearly with the scale factor.

A quadrilateral P is enlarged by a scale factor of 1.2 to give quadrilateral Q. The area of quadrilateral P is 20 cm². Calculate the area of quadrilateral Q.

Learn how to calculate the area of a quadrilateral after enlargement by a scale factor of 1.2. This step-by-step solution demonstrates the relationship between the original and enlarged shapes. Suitable for students in Grades 6-8.

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