Question

What’s the area of the base of a rectangular prism with a length of 7 1/4 m, a width of 10 1/2m, and a height of 12 2/5 m, the answer should be a mixed number in simplest form, only find the area of the base

Answer 1

To find the area of the base of a rectangular prism, we multiply the length by the width. Given the dimensions:

- Length \( = 7 \frac{1}{4} \, \text{m} = \frac{29}{4} \, \text{m} \)
- Width \( = 10 \frac{1}{2} \, \text{m} = \frac{21}{2} \, \text{m} \)

Now, we can calculate the area of the base:

\[
\text{Area} = \text{Length} \times \text{Width} = \left( \frac{29}{4} \right) \times \left( \frac{21}{2} \right)
\]

To multiply these fractions:

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

Next, we convert \(\frac{609}{8}\) into a mixed number. We perform the division \(609 \div 8\):

\[
609 \div 8 = 76 \quad \text{(with a remainder of 1)}
\]

So, we can express \(\frac{609}{8}\) as:

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

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

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