Formula for the volume of the oblique prism is:
[tex] V=A_{\text{base}}\cdot H [/tex].
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,
[tex] h^2+3^2=5^2,\\ h^2=25-9=16,\\ h=4 [/tex].
2. The area of the base is given by formula
[tex] A_{\text{base}}=\dfrac{1}{2} a\cdot h=\dfrac{1}{2}\cdot 6\cdot4=12 [/tex] sq. un.
Thus, the volum is V=12·12=144 cubic units.
