Answer:
A prism is a solid object having two identical bases, hence the same cross section along the length. This is a rectangular prism its base is a rectangle. multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:
[tex]V=L\times W\times H[/tex]
Therefore, Associative Property can be used to mentally find the volume of the prisms shown by selecting the easier way of the multiplication. For instance, we can say that:
[tex]L=5cm \\ \\ W=18cm \\ \\ H=20cm[/tex]
In whose case:
[tex]V=5\times 18\times 20[/tex]
To operate this mentally is not an easy way, but what if we rotate this shape? so we say that:
[tex]L=18cm \\ \\ W=20cm \\ \\ H=5cm[/tex]
Then, the volume can be found as:
[tex]V=18\times 20\times 5[/tex]
There are two forms of finding the result. First, multiplying 18 by 20 and then the result by 5, but as in the previous case this is a tricky way to do mentally:
[tex]V=(18\times 20)\times 5[/tex]
Hence, here we can use Associative Property multiplying 20 by 5 and then the result by 18:
[tex]V=18\times (20\times 5)[/tex]
This last arrangement is easier because 20 x 5 is easy to remember given that the result is 100. Then, by multiplying this result by 18 then we get 1800.
