we know that
The volume of the prism is equal to
[tex]V=B*h[/tex]
where
B is the area of the base
h is the height of the prism
Step 1
Find the area of the rectangular base
we know that
the area of a rectangle is equal to
[tex]A=L*W[/tex]
In this problem we have
[tex]L=13\ units[/tex]
[tex]W=10\ units[/tex]
[tex]A=13*10=130\ units^{2}[/tex]
Step 2
Find the height of the prism
Applying the Pythagoras Theorem
[tex]17^{2}=8^{2} +h^{2}[/tex]
solve for h
[tex]h^{2}=17^{2}-8^{2}[/tex]
[tex]h^{2}=225[/tex]
[tex]h=15\ units[/tex]
Step 3
Find the volume of the prism
The volume of the prism is equal to
[tex]V=B*h[/tex]
substitute the values
[tex]V=130*15=1,950\ units^{3}[/tex]
therefore
the answer is
[tex]1,950\ units^{3}[/tex]
