To find the volume of the rectangular prism, we need to follow these steps:
1. Identify the height of the prism:
The height of the rectangular prism is given as [tex]\(\frac{2}{5} \, m\)[/tex].
2. Convert the area of the square base to an improper fraction and then to a decimal:
The area of the square base is given as [tex]\(2 \frac{4}{5} \, m^2\)[/tex]. First, convert this mixed number to an improper fraction.
[tex]\(2 \frac{4}{5} = 2 + \frac{4}{5} = \frac{10}{5} + \frac{4}{5} = \frac{14}{5}\)[/tex]
Now, convert the improper fraction to a decimal value:
[tex]\[
\frac{14}{5} = 2.8
\][/tex]
So, the area of the square base is [tex]\(2.8 \, m^2\)[/tex].
3. Calculate the volume of the rectangular prism:
The volume [tex]\(V\)[/tex] of a rectangular prism is calculated by multiplying the height [tex]\(h\)[/tex] by the area of the base [tex]\(A\)[/tex]:
[tex]\[
V = h \times A
\][/tex]
Substitute the given values:
[tex]\[
V = \left( \frac{2}{5} \, m \right) \times \left( 2.8 \, m^2 \right)
\][/tex]
Now, perform the multiplication:
[tex]\[
\frac{2}{5} \times 2.8 = 0.4 \times 2.8 = 1.12
\][/tex]
Therefore, the volume of the rectangular prism is:
[tex]\[
V = 1.12 \, m^3
\][/tex]
So, the volume of the rectangular prism is [tex]\(1.12 \, m^3\)[/tex].
