Question 603142
The base is a right triangle with a hypotenuse measuring 5 inches and a leg measuring 3 inches.
According to Pythagoras theorem, the other leg must measure 4 inches, because
{{{3^2+4^2=5^2}}} {{{drawing(300,300,-0.5,4.5,-1.5,3.5,
triangle(0,0,0,3,4,0),rectangle(0,0,0.15,0.15),
locate(1.8,-0.05,4),locate(0.05,1.6,3), locate(2,1.75,5)
)}}}
The triple 3,4,5 is the best known and most popular of the Pythagorean triples, those sets of 3 positive integers with the square of the largest equal to the sum of the squares of the other two.
So the base of that pyramid is a triangle with two perpendicular sides measuring 3 and 4 inches. Calling one of them the base of the triangle, and the other one the height of the triangle, the area of the triangle, In square inches, is calculated as
{{{(1/2)*3*4=6}}}
The volume of a pyramid is 1/3 times the area of the base, times the height of the pyramid.
For the pyramid in the problem, the volume, in cubic inches, is
{{{Volume=(1/3)*6*8=16}}}