Question

To use the formula V=Bh to find the volume of a rectangular prism, you must first find the area of the base, B. What is the area of the base of a rectangular prism with a length of 7 1/4m, a width of 10 1/2m, and a height of 12 2/5m? Your answer should be a mixed number in simplest form. Please make sure you only find the area of the base (B).(1 point)

Answer 1

To find the area of the base \( B \) of a rectangular prism, you can use the formula:

\[ B = \text{length} \times \text{width} \]

First, we need to convert the mixed numbers for the length and width into improper fractions.

1. Convert the length \( 7 \frac{1}{4} \) m: \[ 7 \frac{1}{4} = 7 \times 4 + 1 = 28 + 1 = 29 \quad \text{(improper fraction: } \frac{29}{4}\text{)} \]

2. Convert the width \( 10 \frac{1}{2} \) m: \[ 10 \frac{1}{2} = 10 \times 2 + 1 = 20 + 1 = 21 \quad \text{(improper fraction: } \frac{21}{2}\text{)} \]

Now, substitute the improper fractions into the area formula:

\[ B = \frac{29}{4} \times \frac{21}{2} \]

To multiply the fractions, multiply the numerators and the denominators:

\[ B = \frac{29 \times 21}{4 \times 2} = \frac{609}{8} \]

Now, convert \( \frac{609}{8} \) into a mixed number.

1. Divide 609 by 8:

\[ \text{609 divided by 8} = 76 \quad \text{(since } 76 \times 8 = 608\text{)} \]

• The remainder is \( 609 - 608 = 1 \).

Thus, we have:

\[ \frac{609}{8} = 76 \frac{1}{8} \]

Therefore, the area of the base \( B \) of the rectangular prism is:

\[ \boxed{76 \frac{1}{8}} \quad \text{m}^2 \]