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 6 1/4m, a width of 5 1/2m, and a height of 2 2/5m? Your answer should be a mixed number in simplest form.

Answer 1

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

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

The given dimensions are:

- Length = \( 6 \frac{1}{4} \) meters
- Width = \( 5 \frac{1}{2} \) meters

First, we convert the mixed numbers into improper fractions.

For the length:

\[
6 \frac{1}{4} = 6 + \frac{1}{4} = \frac{6 \times 4}{4} + \frac{1}{4} = \frac{24}{4} + \frac{1}{4} = \frac{25}{4}
\]

For the width:

\[
5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{5 \times 2}{2} + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2}
\]

Now we calculate the area \( B \):

\[
B = \frac{25}{4} \times \frac{11}{2}
\]

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

\[
B = \frac{25 \times 11}{4 \times 2} = \frac{275}{8}
\]

Next, we convert \( \frac{275}{8} \) into a mixed number. We divide 275 by 8:

\[
275 \div 8 = 34 \quad \text{(whole number part)}
\]
\[
275 - (34 \times 8) = 275 - 272 = 3 \quad \text{(remainder)}
\]

So, we can write:

\[
\frac{275}{8} = 34 \frac{3}{8}
\]

Thus, the area of the base of the rectangular prism is:

\[
\boxed{34 \frac{3}{8}} \text{ square meters}
\]