Question

the volume of a prism which has an altitude of 10 units and has a right triangle base with a hypotenuse of 13 units and a leg of 12 units is

Answer 1

Check the picture below.

since we know the hypotenuse and one of the legs of the triangular base, we can use the pythagorean theorem to get the missing leg, namely the base of the triangle, as you see in the picture.  Thus we end up with a triangle whose base is 5 and height is 12.

now, the volume of the prims, is just the area of its triangular base, times the length, namely 10.

$\bf \textit{volume of the triangular prism}\\\\ V=\stackrel{length}{(10)}\stackrel{base's~area}{\left[ \cfrac{1}{2}(5)(12) \right]}$