To find the area of the postcard, we need to know its width in addition to its length. The length of the postcard is given as 15 centimeters. However, since we don't have the width, we can reasonably assume that the postcard maintains the same aspect ratio as the original photo (6 cm by 4 cm).
First, we can calculate the aspect ratio of the original photo:
- The width of the original photo is 4 cm, and the length is 6 cm.
- The aspect ratio (width to length) is \( \frac{4}{6} = \frac{2}{3} \).
If we let the width of the new postcard be \( w \), then using the aspect ratio we have:
\[ \frac{w}{15} = \frac{2}{3}. \]
To find \( w \), we can cross-multiply:
\[ 3w = 2 \times 15. \] \[ 3w = 30. \] \[ w = \frac{30}{3} = 10 \text{ cm}. \]
Now we can calculate the area of the postcard using the formula for area:
\[ \text{Area} = \text{length} \times \text{width} = 15 \text{ cm} \times 10 \text{ cm} = 150 \text{ square centimeters}. \]
Therefore, the area of the postcard is:
150 square centimeters.