To find the area of a right triangle, you can use the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base is \(1 \frac{1}{2}\) centimeters and the height is \(2 \frac{1}{2}\) centimeters.
First, let's convert the mixed numbers to improper fractions:
- The base \(1 \frac{1}{2} = \frac{3}{2}\) centimeters.
- The height \(2 \frac{1}{2} = \frac{5}{2}\) centimeters.
Now we can plug these values into the area formula:
\[ \text{Area} = \frac{1}{2} \times \frac{3}{2} \times \frac{5}{2} \]
Calculating this step by step:
-
Multiply the fractions: \[ \frac{3}{2} \times \frac{5}{2} = \frac{15}{4} \]
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Multiply by \(\frac{1}{2}\): \[ \text{Area} = \frac{1}{2} \times \frac{15}{4} = \frac{15}{8} \]
Now convert \(\frac{15}{8}\) to a mixed number:
\(\frac{15}{8} = 1 \frac{7}{8}\).
Therefore, the area of the tile is:
\[ \boxed{1 \frac{7}{8}} \text{ square centimeters} \]