Triangular Prism:
\(\sf~V=\dfrac{1}{2}\times~l\times~w\times~h\)
\(\sf~V=\dfrac{1}{2}\times7\times3\times3\)
\(\sf~V=3.5\times3\times3\)
\(\sf~V=10.5\times3\)
\(\sf~V=31.5\)
Break the Trapezoidal Prism into a rectangular prism with side measurements of 12, 18, and 6 and into a triangular prism with measurements of 6, 16, and 12.
Rectangular Prism:
\(\sf~V=lwh\)
\(\sf~V=(12)(18)(6)\)
Multiply all 3 numbers together:
\(\sf~V=1296\)
Now find the volume of the triangular prism:
\(\sf~V=\dfrac{1}{2}lwh\)
\(\sf~V=\dfrac{1}{2}(6)(16)(12)\)
Multiply all 4 numbers:
\(\sf~V=576\)
Add the two volumes together:
\(\sf1296+576=1872\)
Now we have to get rid of the area inside.
It's two rectangles both with lengths of 12 and widths of 6.
\(\sf~A=lw\)
\(\sf~A=(12)(6)\)
\(\sf~A=72\)
Multiply by 2 then subtract from the total volume we got:
\(\sf~72\times2 = 144\)
Subtract it:
\(\sf1872-144=1728\)
