Question

A piece of a tile is in the shape of a right triangle. The base is 1 1/2 centimeters and the height is 2 1/2 centimeters. What is the area in square centimeters?
A. 8 square centimeters
B. 1 7/8 square centimeters
C. 3 3/4 square centimeters
D. 4 square centimeters

Answer 1

The area \( A \) of a right triangle can be calculated using the formula:

\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

In this case, the base is \( 1 \frac{1}{2} \) centimeters and the height is \( 2 \frac{1}{2} \) centimeters. First, let's convert these mixed numbers to improper fractions.

1. Convert \( 1 \frac{1}{2} \):
\[
1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}
\]

2. Convert \( 2 \frac{1}{2} \):
\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}
\]

Now we can substitute these values into the area formula:

\[
A = \frac{1}{2} \times \frac{3}{2} \times \frac{5}{2}
\]

Calculate the multiplication step-by-step:

1. First calculate \( \frac{3}{2} \times \frac{5}{2} \):
\[
\frac{3 \cdot 5}{2 \cdot 2} = \frac{15}{4}
\]

2. Now multiply this result by \( \frac{1}{2} \):
\[
A = \frac{1}{2} \times \frac{15}{4} = \frac{15}{8}
\]

Next, we will convert \( \frac{15}{8} \) into a mixed number:

\[
\frac{15}{8} = 1 \frac{7}{8}
\]

Thus, the area of the tile in square centimeters is:

\[
1 \frac{7}{8} \quad \text{square centimeters}
\]

The correct answer is:

**B. \( 1 \frac{7}{8} \) square centimeters**