Question

Find the volume of the oblique prism. 

Answer 1

Formula for the volume of the oblique prism is:

$V=A_{\text{base}}\cdot H$.

From the diagram H=12 units and the base is isosceles triangle with lengths of the sides 5, 5 and 6 units.

1. Find the length of the altitude h to the largest side. In isosceles triangle the altitude to the base is also the median, so it divides the base into two equal parts. By the Pythagorean theorem,

$h^2+3^2=5^2,\\ h^2=25-9=16,\\ h=4$.

2. The area of the base is given by formula

$A_{\text{base}}=\dfrac{1}{2} a\cdot h=\dfrac{1}{2}\cdot 6\cdot4=12$ sq. un.

Thus, the volum is V=12·12=144 cubic units.