Let's solve the problem step-by-step:
1. Original Area: We start with the original area of the shape, which is given as [tex]\( 6 \, \text{cm}^2 \)[/tex].
2. Scale Factor: The shape is enlarged by a scale factor of 4. This means that every linear dimension (length, width, height, etc.) of the shape is multiplied by 4.
3. Effect on Area: When you enlarge a shape by a scale factor, the new area is found by multiplying the original area by the square of the scale factor. This is because area is a two-dimensional measurement, and scaling affects both dimensions.
4. Calculation:
- The scale factor is [tex]\(4\)[/tex].
- The square of the scale factor is [tex]\( 4^2 = 16 \)[/tex].
5. New Area: To find the area of the enlarged shape, we multiply the original area by the square of the scale factor:
[tex]\[
\text{New Area} = \text{Original Area} \times (\text{Scale Factor})^2
\][/tex]
Substituting in the given values:
[tex]\[
\text{New Area} = 6 \, \text{cm}^2 \times 16
\][/tex]
6. Result:
[tex]\[
\text{New Area} = 96 \, \text{cm}^2
\][/tex]
So, the area of the new shape is [tex]\( 96 \, \text{cm}^2 \)[/tex].
