To find the area of a right triangle, you can use the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Given the base is \( 1 \frac{1}{2} \) centimeters and the height is \( 2 \frac{1}{2} \) centimeters, we first convert these mixed numbers into improper fractions:
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The base \( 1 \frac{1}{2} \) can be converted as follows: \[ 1 \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \]
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The height \( 2 \frac{1}{2} \) can be converted as follows: \[ 2 \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \]
Now we 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:
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Multiply the fractions: \[ \frac{3}{2} \times \frac{5}{2} = \frac{15}{4} \]
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Now multiply by \( \frac{1}{2} \): \[ \frac{1}{2} \times \frac{15}{4} = \frac{15}{8} \]
Next, we need to convert \( \frac{15}{8} \) to a mixed number:
\[ 15 \div 8 = 1 \quad \text{(with a remainder of 7)} \] So,
\[ \frac{15}{8} = 1 \frac{7}{8} \]
Thus, the area of the triangle is \( 1 \frac{7}{8} \) square centimeters.
Therefore, the correct response is:
1 \( \frac{7}{8} \) square centimeters.